{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Quantitative Finance\n",
    "\n",
    "Copyright (c) 2019 Python Charmers Pty Ltd, Australia, <https://pythoncharmers.com>. All rights reserved.\n",
    "\n",
    "<img src=\"img/python_charmers_logo.png\" width=\"300\" alt=\"Python Charmers Logo\">\n",
    "\n",
    "Published under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. See `LICENSE.md` for details.\n",
    "\n",
    "Sponsored by Tibra Global Services, <https://tibra.com>\n",
    "\n",
    "<img src=\"img/tibra_logo.png\" width=\"300\" alt=\"Tibra Logo\">\n",
    "\n",
    "\n",
    "## Module 1.1: Distributions and Random Processes\n",
    "\n",
    "### 1.1.2: Distributions\n",
    "\n",
    "Many real world phenomena can be modelled with random variables, which is particularly useful when we do not have all possible information about a given environment. Consider a die roll, where we throw a die into the air, and see which number is on top.\n",
    "\n",
    "The die has six possible outcomes: 1, 2, 3, 4, 5 and 6, which are the possible states or values. It is impossible* to get a value other than these six distinct possible.\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    * Some might argue that it would be possible to properly model a die throw and know what the result would be. Whether it is possible is the type of question that keeps physicists up at night, however it almost certainly would be more effort than it's worth.\n",
    "</div>\n",
    "\n",
    "Here is a simulation of a die roll."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "possible_states = [1, 2, 3, 4, 5, 6]\n",
    "\n",
    "random.choice(possible_states)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we run this simulation 100,000 times, we can get an *empirical estimate* of the distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "NUM_TRIALS = 100000\n",
    "\n",
    "results = [random.choice(possible_states) for i in range(NUM_TRIALS)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({4: 16616, 3: 16572, 1: 16629, 5: 16792, 6: 16768, 2: 16623})"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from collections import Counter\n",
    "counts = Counter(results)\n",
    "counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RendererRegistry.enable('default')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import altair as alt\n",
    "alt.renderers.enable('default')  # Setup your environment to show altair plots.  Note this option depends on where you are running your code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   state  count\n",
      "0      1  16629\n",
      "1      2  16623\n",
      "2      3  16572\n",
      "3      4  16616\n",
      "4      5  16792\n",
      "5      6  16768\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-81e8c880bf3f436aade657ceeab801cb.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-81e8c880bf3f436aade657ceeab801cb.vega-embed details,\n",
       "  #altair-viz-81e8c880bf3f436aade657ceeab801cb.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-81e8c880bf3f436aade657ceeab801cb\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-81e8c880bf3f436aade657ceeab801cb\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-81e8c880bf3f436aade657ceeab801cb\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.20.1?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.20.1\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"name\": \"data-aac2c504215e97530bfeff192a0aa6d4\"}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"field\": \"state\", \"type\": \"ordinal\"}, \"y\": {\"field\": \"count\", \"type\": \"quantitative\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.20.1.json\", \"datasets\": {\"data-aac2c504215e97530bfeff192a0aa6d4\": [{\"state\": 1, \"count\": 16629}, {\"state\": 2, \"count\": 16623}, {\"state\": 3, \"count\": 16572}, {\"state\": 4, \"count\": 16616}, {\"state\": 5, \"count\": 16792}, {\"state\": 6, \"count\": 16768}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "die_rolls = pd.DataFrame({\n",
    "    'state': possible_states,\n",
    "    'count': [counts.get(state, 0) for state in possible_states]\n",
    "})\n",
    "\n",
    "print(die_rolls)\n",
    "\n",
    "alt.Chart(die_rolls).mark_bar().encode(\n",
    "    x='state:O',\n",
    "    y='count'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As one might expect with a \"fair\" die roll like this, the estimates are about the same (your results may vary).\n",
    "\n",
    "More formally, we have a random variable $X$ such that the value of $X$ is the result of rolling a fair die. The distribution of $X$ is the following:\n",
    "\n",
    "\n",
    "$\n",
    "\\begin{gather*}\n",
    "  P(X=x) = \\begin{cases}\n",
    "  \\frac{1}{6} & \\text{if $x \\in \\{1,2,3,4,5,6\\}$}\\\\\n",
    "  0 & \\text{otherwise.}\n",
    "  \\end{cases}\n",
    "\\end{gather*}\n",
    "$\n",
    "\n",
    "In this case, all options (at least, the valid ones) have the same likelihood of appearing, and therefore the resulting distribution is known as a *uniform distribution*. Uniform distributions can occur for both discrete and continuous variables.\n",
    "\n",
    "A **discrete** variable is one that takes on a fixed set of values, such as a die roll or the month you were born. They are usually finite (i.e. there is only so many of them), but the requirement is technically that they be *countable*, which allows for infinite discrete values (think of the integers as a discrete infinite random variable).\n",
    "\n",
    "A **continuous** variable is one that can take on an arbitrary value. As an example, the amount of liquid in a cup is continuous. It can be 350ml, or 350.1ml, or 350.1252342ml, or so on, with infinite precision (we will ignore the effect of the Planck constant). \n",
    "\n",
    "Distributions exist for both discrete random variables, as we saw above, and for continuous random variables, however they often behave differently."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!-- Run me, but there is  need to worry about this code - \n",
       "    it makes the equation in the next cell larger and more readable -->\n",
       "<style>\n",
       "    .big_function {font-size: 200%;}\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%html\n",
    "<!-- Run me, but there is  need to worry about this code - \n",
    "    it makes the equation in the next cell larger and more readable -->\n",
    "<style>\n",
    "    .big_function {font-size: 200%;}\n",
    "</style>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normal Distributions\n",
    "Let's create a normal distribution, which is a continuous distribution centred around 0 and with a standard deviation of 1.\n",
    "\n",
    "A normal distribution is the most commonly seen continuous distribution, and the one most people are familiar with. The equation for the graph is:\n",
    "\n",
    "$$y = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's plot that out\n",
    "import numpy as np\n",
    "x = np.linspace(-5, 5, 1000)  # 1000 linearly spaced points starting -5 going to 5\n",
    "\n",
    "mean = 0\n",
    "sigma = 1\n",
    "\n",
    "y = (1 / np.sqrt(2 * np.pi * sigma ** 2)) * np.e ** -((x - mean) ** 2) / (2 * sigma ** 2)\n",
    "\n",
    "# Or a bit more nicely laid out...\n",
    "\n",
    "scale_term = (1 / np.sqrt(2 * np.pi * sigma ** 2))\n",
    "exponent_term = ((x - mean) ** 2) / (2 * sigma ** 2)\n",
    "y = scale_term * np.e ** -exponent_term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "plt.plot(x, y, \"-\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = stats.norm(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.77053819, -0.60089593, -0.45477577,  0.66173876, -0.50521691,\n",
       "       -2.12192442, -0.4218337 , -1.72082043,  0.3610369 ,  0.78881818])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate 10 random variates from this distribution\n",
    "n.rvs(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# note that Counter isn't very helpful here. It is *highly* likely that all counts will be 1\n",
    "# regardless of how many values you generate. In fact, it's nearly impossible to get the same value twice.\n",
    "results = n.rvs(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({-3.5638515920746605: 1,\n",
       "         0.4520758024166038: 1,\n",
       "         1.8308440239137487: 1,\n",
       "         0.8332257130371589: 1,\n",
       "         -1.3615243776836115: 1,\n",
       "         0.6630576469908436: 1,\n",
       "         -0.917976084454392: 1,\n",
       "         0.8753430504886834: 1,\n",
       "         -1.1596425272663522: 1,\n",
       "         0.29099779183573965: 1})"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Counter(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-abb742a677bc489aa60e0a26367fd5df.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-abb742a677bc489aa60e0a26367fd5df.vega-embed details,\n",
       "  #altair-viz-abb742a677bc489aa60e0a26367fd5df.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-abb742a677bc489aa60e0a26367fd5df\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-abb742a677bc489aa60e0a26367fd5df\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-abb742a677bc489aa60e0a26367fd5df\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.20.1?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.20.1\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"name\": \"data-1c859b41c757a52789963ea4c9ad1aae\"}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"color\": {\"value\": \"#287E1E\"}, \"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.20.1.json\", \"datasets\": {\"data-1c859b41c757a52789963ea4c9ad1aae\": [{\"value\": 0.40312683322805987}, {\"value\": -0.9605652275403992}, {\"value\": 1.1200298818329473}, {\"value\": -1.03164349508992}, {\"value\": -0.982103442179831}, {\"value\": -1.6153653711530787}, {\"value\": 0.020060276400548752}, {\"value\": -0.5577753535168603}, {\"value\": 1.2268326200660067}, {\"value\": 0.2680870200088908}, {\"value\": 0.553789492152773}, {\"value\": -1.0074007948482695}, {\"value\": 0.19681202899369543}, {\"value\": -1.1532290732834805}, {\"value\": 0.040096664070366855}, {\"value\": -0.6437000212396596}, {\"value\": -0.07373298641167252}, {\"value\": 1.1855481443118807}, {\"value\": 0.2816550406877894}, {\"value\": -2.181099562433481}, {\"value\": 0.8251413013132762}, {\"value\": -0.7421367177542963}, {\"value\": 0.6815742324926334}, {\"value\": 0.24489606635556635}, {\"value\": -1.5350275326231864}, {\"value\": 0.018396602056723495}, {\"value\": 0.45012720798067984}, {\"value\": -0.5226121662870167}, {\"value\": 0.18643432576141514}, {\"value\": -0.10914696346124698}, {\"value\": 0.00588948905193463}, {\"value\": -1.39474519920975}, {\"value\": 0.15579527040505}, {\"value\": 1.0858199153974144}, {\"value\": -0.12284324306382273}, {\"value\": 0.7277001416050489}, {\"value\": -0.14242267270135361}, {\"value\": 0.9178045416896534}, {\"value\": 0.04785337944759804}, {\"value\": 1.6383931748724634}, {\"value\": -0.3782508601638067}, {\"value\": -0.4313396265870602}, {\"value\": 0.9915971366336833}, {\"value\": 2.4009084962084195}, {\"value\": 0.978182540832251}, {\"value\": 0.4041568922015944}, {\"value\": 0.3274712454040804}, {\"value\": 0.871938528777414}, {\"value\": -0.24292911419036178}, {\"value\": -0.17837267568341658}, {\"value\": 0.13277399637539303}, {\"value\": -0.10615844101060462}, {\"value\": 0.015583788417199675}, {\"value\": 0.9393194775987499}, {\"value\": -1.7399953370494832}, {\"value\": 1.2227202202943563}, {\"value\": -1.2933855249163464}, {\"value\": -0.8738526177665793}, {\"value\": -0.624413949291709}, {\"value\": 1.1649130368880904}, {\"value\": -0.41580175748590703}, {\"value\": -1.6450032114717714}, {\"value\": 0.8436483497914525}, {\"value\": -1.937762216357533}, {\"value\": 1.9353990168530726}, {\"value\": -0.6180481347482154}, {\"value\": 0.22384435989088156}, {\"value\": 1.056201217939647}, {\"value\": -0.38370912890578573}, {\"value\": -1.759725435266534}, {\"value\": 1.0289747525468986}, {\"value\": 2.057445436703376}, {\"value\": 0.038382756730337274}, {\"value\": -1.1688197062412105}, {\"value\": -0.38276010673589056}, {\"value\": -0.28620756789529805}, {\"value\": 0.6087508351542351}, {\"value\": -1.8751221983572406}, {\"value\": -1.544605822279338}, {\"value\": 1.5640942042200907}, {\"value\": 0.3893614000924562}, {\"value\": -0.5434652441984464}, {\"value\": 0.5306917258832535}, {\"value\": -1.599703467890791}, {\"value\": -1.6022187053685484}, {\"value\": -0.39128817291010837}, {\"value\": -1.0748099088420167}, {\"value\": -1.094782519053807}, {\"value\": 0.3816604719568802}, {\"value\": -0.24559889007097943}, {\"value\": 0.07297181721756286}, {\"value\": 0.48286785320199205}, {\"value\": -0.6851519161369914}, {\"value\": 0.5384944533980413}, {\"value\": -0.5991473563402373}, {\"value\": 1.8909438838452135}, {\"value\": -0.4292682773920039}, {\"value\": -0.9311512271652498}, {\"value\": -0.8415736108664945}, {\"value\": -0.7236044460719917}, {\"value\": 2.1773934066209923}, {\"value\": -0.9308422605103778}, {\"value\": -1.2222367490096686}, {\"value\": 0.5821949280269217}, {\"value\": -0.27057435386943635}, {\"value\": 0.6406348108678622}, {\"value\": -0.9653043923363313}, {\"value\": 0.9117001754227819}, {\"value\": 0.5112065017637137}, {\"value\": 0.9330297714579748}, {\"value\": -0.6739498389966739}, {\"value\": -1.3510389974406947}, {\"value\": -1.3694154846096476}, {\"value\": 0.2167318120886079}, {\"value\": -1.2524742574778585}, {\"value\": 2.1373108467058652}, {\"value\": 0.8900430240895043}, {\"value\": 0.4070929241907765}, {\"value\": -0.08999186248122022}, {\"value\": 0.030532265223717943}, {\"value\": -0.5132482259008004}, {\"value\": -1.1240713696500477}, {\"value\": 0.52344489268}, {\"value\": 1.268116169373447}, {\"value\": 0.73439010263678}, {\"value\": -0.7042628772401222}, {\"value\": 0.5268913485078832}, {\"value\": -1.433353862112669}, {\"value\": 1.3172488366935844}, {\"value\": 1.7401528454401252}, {\"value\": -0.7606536791953364}, {\"value\": 0.2834876500952593}, {\"value\": 1.1144282041788374}, {\"value\": 0.37136355346138045}, {\"value\": 0.6985447914285521}, {\"value\": 1.000866077814393}, {\"value\": -0.9855974618915567}, {\"value\": -0.32769135107426023}, {\"value\": -0.3454711970147464}, {\"value\": -0.3623128152411635}, {\"value\": 1.5307834852094169}, {\"value\": 0.8104820472825325}, {\"value\": 0.8615188757922616}, {\"value\": 1.1063312664484124}, {\"value\": 1.368105600319646}, {\"value\": 0.35808178012679626}, {\"value\": -0.8446395230961116}, {\"value\": 0.3462946007736147}, {\"value\": 0.509580634271385}, {\"value\": 0.6886384311463319}, {\"value\": 0.22874006682664327}, {\"value\": -2.773881797252371}, {\"value\": 1.2078846349816779}, {\"value\": 0.27468147456668934}, {\"value\": 0.5638784307141718}, {\"value\": -1.0240031368659015}, {\"value\": 0.018682982779437515}, {\"value\": -1.004019733327108}, {\"value\": -0.19315412588474035}, {\"value\": 1.577535691943158}, {\"value\": -1.3780071076564702}, {\"value\": 0.3246095021354694}, {\"value\": -0.5022026199132142}, {\"value\": -0.39307237427270764}, {\"value\": 1.937377847170624}, {\"value\": 0.7810307664174054}, {\"value\": -0.8635008142900644}, {\"value\": -0.6937415626204491}, {\"value\": 1.2480276020218186}, {\"value\": 2.0221200265431976}, {\"value\": -1.1843277862913961}, {\"value\": 0.935111247880633}, {\"value\": -1.6579494803919053}, {\"value\": -0.5526075810586142}, {\"value\": 0.026823605741445575}, {\"value\": -1.0004301437824488}, {\"value\": 0.600700404814859}, {\"value\": 1.2206869060302572}, {\"value\": -0.8946260635135285}, {\"value\": 0.05722952497756111}, {\"value\": -1.4730378729718283}, {\"value\": 0.9815356263756949}, {\"value\": -0.713914204872861}, {\"value\": 0.15239731330995743}, {\"value\": 1.4916083391416026}, {\"value\": 1.3201655710585258}, {\"value\": -1.1112790123285248}, {\"value\": 0.6424825712485055}, {\"value\": 0.2789454254579421}, {\"value\": 0.2469957744361006}, {\"value\": 3.6477849236612743}, {\"value\": -0.8646188748825357}, {\"value\": 0.07669528912932536}, {\"value\": -0.8778537930854416}, {\"value\": 0.2317866641503014}, {\"value\": -0.17045367620996374}, {\"value\": 0.7824163867537514}, {\"value\": 0.6869643581070908}, {\"value\": 1.3796114984160137}, {\"value\": 0.1840165135324537}, {\"value\": -0.3429295637118256}, {\"value\": 0.932509738070924}, {\"value\": 1.1831636528398695}, {\"value\": -2.0452354433402515}, {\"value\": 0.36428274563389995}, {\"value\": -0.8291174596860251}, {\"value\": -0.44199383819865273}, {\"value\": -1.0790776662408468}, {\"value\": -0.2972233759065755}, {\"value\": 2.402955080265031}, {\"value\": 0.5193977568045721}, {\"value\": -0.7546059908675131}, {\"value\": 0.14827460116984326}, {\"value\": 0.8548815190852596}, {\"value\": -0.6445260241816128}, {\"value\": 0.46448238400851666}, {\"value\": 2.0126058561509863}, {\"value\": 0.540814483599858}, {\"value\": -0.034777765049964715}, {\"value\": -0.30714847221775743}, {\"value\": -1.8078296151003168}, {\"value\": 0.6998084996750873}, {\"value\": -0.331251590879986}, {\"value\": 0.7498757797634091}, {\"value\": 0.9236872880122149}, {\"value\": 0.5858393212828753}, {\"value\": 0.45476194064579056}, {\"value\": -0.22210745784365288}, {\"value\": 0.20655518210986368}, {\"value\": -0.10045980795466124}, {\"value\": -0.0515288384881233}, {\"value\": -0.07644181074386604}, {\"value\": -0.29118296116788095}, {\"value\": 1.9615577599881933}, {\"value\": -0.3410782142606597}, {\"value\": -1.150494483504702}, {\"value\": 0.856186227094976}, {\"value\": 0.0022803279810317064}, {\"value\": -0.6186901011528638}, {\"value\": 1.8046766199321866}, {\"value\": 1.2557107809134112}, {\"value\": 2.123350227861207}, {\"value\": 0.3846285007762231}, {\"value\": 0.7769497026691823}, {\"value\": -0.8599616492562995}, {\"value\": -0.3055764809416685}, {\"value\": -2.212220877063864}, {\"value\": -0.06942592872939185}, {\"value\": 0.08545262894265478}, {\"value\": 0.03140860849792559}, {\"value\": 1.0598504549242895}, {\"value\": -0.41219734201910946}, {\"value\": -0.5026429768357789}, {\"value\": 0.98207854088042}, {\"value\": -0.6074893016750076}, {\"value\": 0.346437538908916}, {\"value\": 0.4090174828322062}, {\"value\": -0.2949668264905232}, {\"value\": 0.0036428202098758985}, {\"value\": 0.5962528006252096}, {\"value\": 0.11409114491943464}, {\"value\": 0.2314615439216001}, {\"value\": 1.6889958724449103}, {\"value\": 0.14441890853491188}, {\"value\": -1.6365603723771116}, {\"value\": 0.3393740052883016}, {\"value\": -1.1618163511599118}, {\"value\": -0.20552522872678355}, {\"value\": -0.4589375342207782}, {\"value\": -0.3567559481338721}, {\"value\": 0.2643122857745653}, {\"value\": -0.5151553381880827}, {\"value\": -0.5568533593388847}, {\"value\": 1.7293351055231938}, {\"value\": 0.9848697835200629}, {\"value\": -0.10782878790595599}, {\"value\": -0.4797182179725403}, {\"value\": -0.1868635330778143}, {\"value\": -1.8708103795192697}, {\"value\": 0.17064066217142043}, {\"value\": 0.14583494549000542}, {\"value\": 1.6832597504762368}, {\"value\": -0.48382319649773586}, {\"value\": -0.1410143540903431}, {\"value\": -1.4157525721056659}, {\"value\": 0.3394850121875477}, {\"value\": 0.527286803067513}, {\"value\": 0.6090945380435703}, {\"value\": 0.8096178809284738}, {\"value\": -1.000936747701668}, {\"value\": 1.07788756831608}, {\"value\": -0.2582275336583307}, {\"value\": 2.0670813784171056}, {\"value\": -0.21859683791817544}, {\"value\": 0.01985563703691123}, {\"value\": 1.522633186553659}, {\"value\": -0.41211774640603815}, {\"value\": -0.5306870006399677}, {\"value\": 0.3894069473727301}, {\"value\": 1.013579337855517}, {\"value\": 0.7080038445609855}, {\"value\": 0.6778986199939895}, {\"value\": -0.7644402510535203}, {\"value\": -0.14079780202998865}, {\"value\": 0.49149512069639784}, {\"value\": -0.21555090323397658}, {\"value\": -0.663479791829656}, {\"value\": 1.2303709348864327}, {\"value\": -2.109772409502517}, {\"value\": -0.8277627845835572}, {\"value\": -0.5094191064060849}, {\"value\": -1.2694853797630505}, {\"value\": -0.9294409684221817}, {\"value\": -1.8476346931207768}, {\"value\": 1.25715244724475}, {\"value\": 0.4822600415721158}, {\"value\": -1.4917966071547857}, {\"value\": 0.8148180344653929}, {\"value\": 0.2978395695617143}, {\"value\": 0.014464160520680686}, {\"value\": 0.23683597533990766}, {\"value\": -0.08208868950554861}, {\"value\": -0.0017954199056758055}, {\"value\": 2.1393682655406936}, {\"value\": 1.374937354656073}, {\"value\": 0.47615732302594643}, {\"value\": 1.4220729098370186}, {\"value\": 0.9777456154066044}, {\"value\": -0.2678575215612884}, {\"value\": -1.8787762589271304}, {\"value\": -0.4752299705931379}, {\"value\": -1.6406893770817126}, {\"value\": -0.7454597927466342}, {\"value\": -1.5927681758293644}, {\"value\": -1.0213301998530364}, {\"value\": 0.6917648681124794}, {\"value\": 0.6442471183038585}, {\"value\": 0.4372678424001997}, {\"value\": -0.7135439404291138}, {\"value\": 0.8642382375165488}, {\"value\": 1.9195572189164969}, {\"value\": 0.29530281939176983}, {\"value\": 0.2935702837902554}, {\"value\": -1.0222243617689046}, {\"value\": -1.353779995516578}, {\"value\": 0.4164935006335504}, {\"value\": -0.8320870614026034}, {\"value\": -0.9876638670882584}, {\"value\": 0.9168434434775877}, {\"value\": -0.17329589777513807}, {\"value\": 1.7159461014746553}, {\"value\": 0.052275526756961926}, {\"value\": -0.31270055283593157}, {\"value\": -0.032850926786627}, {\"value\": -0.778777916577251}, {\"value\": -0.5949008350866541}, {\"value\": 0.5365704175844104}, {\"value\": -0.1039891721738332}, {\"value\": 0.4238953130784342}, {\"value\": -0.5701312554272593}, {\"value\": -1.3482393110110158}, {\"value\": 2.0945462224446136}, {\"value\": -0.44212307048725086}, {\"value\": -0.3126223102003596}, {\"value\": -0.059593092236663155}, {\"value\": 0.6686278317709642}, {\"value\": -0.9971366136116161}, {\"value\": -1.2703744207928864}, {\"value\": 2.2927316446114077}, {\"value\": 1.2933698657853252}, {\"value\": -2.036296523498649}, {\"value\": 0.23288940071254083}, {\"value\": 0.9540832881291431}, {\"value\": -0.5405061069644734}, {\"value\": 1.1793991786174833}, {\"value\": -0.7747179317947968}, {\"value\": 0.1315336449197344}, {\"value\": -1.6860263357355494}, {\"value\": 0.9296867569561109}, {\"value\": -0.6229013553008498}, {\"value\": -0.7371810038933759}, {\"value\": -1.9649024151271144}, {\"value\": 0.7674906463970382}, {\"value\": 0.7260943661259972}, {\"value\": -1.3541137200180258}, {\"value\": 0.4630002064228269}, {\"value\": 0.6221621976632642}, {\"value\": 1.510195572291201}, {\"value\": -1.0070667743954167}, {\"value\": 0.5180212976332146}, {\"value\": -0.67073827507871}, {\"value\": -0.30441302005398807}, {\"value\": -0.7553753533831964}, {\"value\": -2.0047031102216852}, {\"value\": -1.0241165018452627}, {\"value\": -0.38857221799354724}, {\"value\": 0.08948012531488088}, {\"value\": -0.9266001115380204}, {\"value\": 0.4031012341516904}, {\"value\": 0.2510603635129218}, {\"value\": 0.44819828423573416}, {\"value\": -1.5324345508333508}, {\"value\": 0.2861660634415162}, {\"value\": -0.6205015461359967}, {\"value\": 0.8249368432592897}, {\"value\": 0.32571448297071603}, {\"value\": 1.4659320771883568}, {\"value\": -0.3629083524626842}, {\"value\": -0.11671354630975168}, {\"value\": -0.0495081859704491}, {\"value\": -0.9014194822364054}, {\"value\": 1.2460381781372942}, {\"value\": 0.6805384623720064}, {\"value\": 1.7860605136100667}, {\"value\": 0.8987078215443199}, {\"value\": -1.6513925181649145}, {\"value\": -0.23606982583940572}, {\"value\": 0.10945197865285203}, {\"value\": 0.45145505463817837}, {\"value\": 0.5334032129116358}, {\"value\": 0.6049146364816425}, {\"value\": 2.292519321309569}, {\"value\": 0.990125656566251}, {\"value\": -0.04435767715566387}, {\"value\": 0.9572511243230224}, {\"value\": -0.33963015682529535}, {\"value\": -0.7085819080174675}, {\"value\": -0.27924273109642006}, {\"value\": 0.9904402963782606}, {\"value\": -1.5569590039177899}, {\"value\": 0.8768210057859702}, {\"value\": 0.13998329760416792}, {\"value\": 0.7899697432942759}, {\"value\": -1.1860222830764902}, {\"value\": 0.8377111528780251}, {\"value\": -0.7075075964341423}, {\"value\": 2.1253203731328063}, {\"value\": 0.09188761512379169}, {\"value\": 1.8589165498863658}, {\"value\": -0.021132067561694542}, {\"value\": -0.31930554182538634}, {\"value\": -0.42896577584842566}, {\"value\": 0.9085781056058753}, {\"value\": 0.4544709047818824}, {\"value\": 0.6641381155340685}, {\"value\": -0.5079573358579137}, {\"value\": 1.1555662098592838}, {\"value\": -2.4438789943656447}, {\"value\": -1.7066249061247751}, {\"value\": -0.1976617947462196}, {\"value\": -0.32778428395100967}, {\"value\": 0.3640001520125797}, {\"value\": 0.5795147309572963}, {\"value\": -0.7764765675944273}, {\"value\": -0.8255573606155454}, {\"value\": 0.01922659476515237}, {\"value\": -0.13170291424772085}, {\"value\": 0.24057999632649543}, {\"value\": 1.231611347396022}, {\"value\": -1.7562363169286657}, {\"value\": 1.8948307698224969}, {\"value\": -0.018938755775393817}, {\"value\": -0.7358836574649248}, {\"value\": -1.4497308964155158}, {\"value\": -0.6636112099372642}, {\"value\": 0.21939527306979825}, {\"value\": -0.24436668617243912}, {\"value\": -0.7765319385081194}, {\"value\": 0.9469936974746296}, {\"value\": -1.5352453756636415}, {\"value\": -0.3073988275586368}, {\"value\": 1.0825341467374683}, {\"value\": -0.3178735661360105}, {\"value\": 0.9738147327303326}, {\"value\": 0.5033557467771573}, {\"value\": -0.39769824017884686}, {\"value\": -0.758323864661392}, {\"value\": -0.7742649917677774}, {\"value\": -0.2454473054528941}, {\"value\": -1.0970618075007235}, {\"value\": 0.6204776072766723}, {\"value\": 0.9400075025178134}, {\"value\": 0.017780045684722086}, {\"value\": 0.8016679146394688}, {\"value\": 1.235010636090474}, {\"value\": -0.10257458408298772}, {\"value\": 0.4975493485428426}, {\"value\": -1.7423930673844417}, {\"value\": -0.40201668499796217}, {\"value\": -0.0752834016402509}, {\"value\": -0.44483119658933284}, {\"value\": -2.2126427747875796}, {\"value\": 0.45434469663526805}, {\"value\": -0.605141259727954}, {\"value\": 0.8503533169499373}, {\"value\": -0.28553847618248895}, {\"value\": -0.5625483902687526}, {\"value\": -0.88952860007178}, {\"value\": -0.6113486748063527}, {\"value\": 0.5250584495792262}, {\"value\": -0.07140226567225685}, {\"value\": -1.401573322476366}, {\"value\": 0.028338976071412985}, {\"value\": 1.6444066129946957}, {\"value\": 0.6503876493082851}, {\"value\": 2.1119792100407078}, {\"value\": 0.01116790825389213}, {\"value\": -0.5613314795008071}, {\"value\": -0.869180820175468}, {\"value\": 0.22077052977167583}, {\"value\": -1.418115106016907}, {\"value\": -0.2627781220646692}, {\"value\": -1.0877765749504824}, {\"value\": -0.6524387897593565}, {\"value\": 0.4438524006566704}, {\"value\": -0.18331544142236866}, {\"value\": 0.9038514528672514}, {\"value\": -0.13031430735606672}, {\"value\": -1.3908686023912924}, {\"value\": -0.9215455353736929}, {\"value\": 1.3769332194173547}, {\"value\": -0.6709805798757872}, {\"value\": 1.2981534635254979}, {\"value\": 0.5594015296920013}, {\"value\": 0.3257659417183334}, {\"value\": -0.6061195652702199}, {\"value\": 1.0537777704290774}, {\"value\": -0.4484145907123186}, {\"value\": 0.9274334681103171}, {\"value\": 0.25992585765508947}, {\"value\": -0.6091824165026788}, {\"value\": -2.079500830438699}, {\"value\": -0.6247254975077171}, {\"value\": 0.6003321758607802}, {\"value\": -0.24927095106966166}, {\"value\": -0.860618484615354}, {\"value\": 0.8322904282251015}, {\"value\": 1.16845337302657}, {\"value\": -1.2338256241095662}, {\"value\": -0.6554030421458208}, {\"value\": 0.08385546779431775}, {\"value\": -1.0490458874364885}, {\"value\": -1.0879030477829332}, {\"value\": -0.32103302022171654}, {\"value\": -0.90957079029565}, {\"value\": -0.9269009207485769}, {\"value\": -1.1341192462170622}, {\"value\": 0.8450152994640535}, {\"value\": 1.6383795690315819}, {\"value\": -0.28488479663956945}, {\"value\": 0.7216003580691885}, {\"value\": -0.3074505192673585}, {\"value\": 0.6681232723602897}, {\"value\": 1.4610781018202752}, {\"value\": -0.7268989889017707}, {\"value\": 2.65754406538431}, {\"value\": -0.24507686729067002}, {\"value\": 0.36192691736611693}, {\"value\": -0.5692950961290292}, {\"value\": 0.24650546884712632}, {\"value\": 1.2025005105460624}, {\"value\": -1.1466790248793293}, {\"value\": 0.2409461356863359}, {\"value\": -1.2299966897580603}, {\"value\": -1.9767134821612797}, {\"value\": -0.5224106874949468}, {\"value\": 2.220256785424165}, {\"value\": 1.3249845970116108}, {\"value\": 0.4502815501327837}, {\"value\": 0.30955113899501996}, {\"value\": 0.07176510257430657}, {\"value\": 0.21676639197671035}, {\"value\": 0.4067768584682505}, {\"value\": -1.2341478042665461}, {\"value\": 0.4715980962090944}, {\"value\": -0.9194151632802899}, {\"value\": 0.4384123506915518}, {\"value\": 0.08612808330856157}, {\"value\": -0.7213895293772357}, {\"value\": 3.897662644993573}, {\"value\": -0.9050796560878251}, {\"value\": -0.1394917917713022}, {\"value\": 0.6360467189599784}, {\"value\": -2.3134206752014967}, {\"value\": 0.36633017833056675}, {\"value\": 0.9450209703046518}, {\"value\": -0.07315071296314098}, {\"value\": -0.6498711927274539}, {\"value\": -0.7707845940698003}, {\"value\": 0.04453413125525696}, {\"value\": -0.4606710935608014}, {\"value\": -0.44308165854952747}, {\"value\": 0.7630872704568813}, {\"value\": -0.012516207756687993}, {\"value\": -0.8282490571544943}, {\"value\": -0.658697648897567}, {\"value\": 0.09273788339907424}, {\"value\": -0.5110767086559792}, {\"value\": 1.1095074393789228}, {\"value\": -0.5936234039736096}, {\"value\": -1.1504861772121595}, {\"value\": 0.8688081637523917}, {\"value\": -1.4684343571838054}, {\"value\": 0.4019970181646502}, {\"value\": -2.3207115934735794}, {\"value\": 1.6741192109354244}, {\"value\": -0.9472429163475395}, {\"value\": 0.11932846487271825}, {\"value\": 0.21225260481581812}, {\"value\": 0.3787272983234326}, {\"value\": 0.854799556620128}, {\"value\": -0.3497632303332667}, {\"value\": 0.6763478482840128}, {\"value\": -0.40925475642752734}, {\"value\": -1.445223982566136}, {\"value\": -0.4219399214034292}, {\"value\": 0.5667319244102902}, {\"value\": 0.3786812695143807}, {\"value\": -1.451740526125655}, {\"value\": -0.2775429788285664}, {\"value\": -1.1119889309526503}, {\"value\": 0.746064855102043}, {\"value\": 1.2912748546011257}, {\"value\": -0.2918091565143055}, {\"value\": -0.16762122837784502}, {\"value\": -0.06373770512049572}, {\"value\": 0.7392020902708138}, {\"value\": 0.6184937224989511}, {\"value\": 1.451418762038814}, {\"value\": -0.5412441973989597}, {\"value\": 0.5012712128164151}, {\"value\": 1.8430060322384696}, {\"value\": 0.49478483068210555}, {\"value\": -1.811227841078559}, {\"value\": -0.44773663061488567}, {\"value\": -0.649154146750948}, {\"value\": -3.081727594233621}, {\"value\": 1.092345904644845}, {\"value\": -0.021040500624139643}, {\"value\": 1.6344062250686808}, {\"value\": -0.2801005509119815}, {\"value\": -0.7330020907171059}, {\"value\": -0.1755091592220964}, {\"value\": 0.9216879079510084}, {\"value\": 0.8835676998638635}, {\"value\": 0.555938444170455}, {\"value\": -1.1052235754298692}, {\"value\": 0.16071217980558317}, {\"value\": -0.46072927667484515}, {\"value\": -0.6440308847504255}, {\"value\": -1.4370385733601518}, {\"value\": 0.9945896558615911}, {\"value\": -0.9379794194774379}, {\"value\": -0.3982683176540585}, {\"value\": -1.5808616996197706}, {\"value\": 0.25982070725414563}, {\"value\": -1.0219622787219544}, {\"value\": -0.44729704420619704}, {\"value\": 1.0610133271565287}, {\"value\": 1.7390285996714359}, {\"value\": -0.9763832417877556}, {\"value\": 1.9672020980312575}, {\"value\": -0.07064652521086633}, {\"value\": -0.5593642356431916}, {\"value\": -0.22396567285347263}, {\"value\": -1.3017743010888099}, {\"value\": -0.19887659868648153}, {\"value\": -0.5498211995290258}, {\"value\": 0.16742605479181907}, {\"value\": 1.2181200022770267}, {\"value\": -0.32673747845671386}, {\"value\": 0.2421318479044695}, {\"value\": -0.7959188016437762}, {\"value\": -0.540785878273468}, {\"value\": -0.14967121814608927}, {\"value\": -0.8146058631463272}, {\"value\": -1.3767604112980745}, {\"value\": -0.03609268154861394}, {\"value\": 0.2741590027812642}, {\"value\": -0.872868735103146}, {\"value\": -0.45354993222860707}, {\"value\": -0.23389974877172034}, {\"value\": -0.5451477221688722}, {\"value\": -0.5608775315500354}, {\"value\": 2.190354387907532}, {\"value\": 0.6757111988863153}, {\"value\": 0.4923642166813232}, {\"value\": 1.6129826599234633}, {\"value\": -1.322990020816935}, {\"value\": 1.0074926892124585}, {\"value\": 0.5831205251510716}, {\"value\": 1.2043427172199574}, {\"value\": -0.016599975849794918}, {\"value\": -0.2787317293684865}, {\"value\": -0.7770993294869126}, {\"value\": 0.4024744836426958}, {\"value\": -0.5159593824361084}, {\"value\": 0.2486636135655997}, {\"value\": -1.1292839290858054}, {\"value\": -2.079682478015309}, {\"value\": 0.15012617068960435}, {\"value\": -0.2832148927708022}, {\"value\": 1.5017030375907827}, {\"value\": 0.14151240943129229}, {\"value\": -0.9468691066789134}, {\"value\": 1.086470630140801}, {\"value\": -0.5454354307719508}, {\"value\": -2.133869141813672}, {\"value\": 1.6450248975955837}, {\"value\": -1.2583352876357805}, {\"value\": 0.1188731337662534}, {\"value\": -0.10819368869904533}, {\"value\": 1.6362703781540953}, {\"value\": -1.5424588109489281}, {\"value\": 0.04481999843933671}, {\"value\": 1.3250793124401876}, {\"value\": -1.571968546697729}, {\"value\": 1.0840751478254704}, {\"value\": -0.3124222143021751}, {\"value\": -0.12874907064648408}, {\"value\": -0.28064098523134723}, {\"value\": -1.0950795689181294}, {\"value\": 0.08644654842634007}, {\"value\": -1.3325723415354653}, {\"value\": 0.37463745567161694}, {\"value\": -0.9197332724237243}, {\"value\": 1.085752615155717}, {\"value\": 0.3666114111246775}, {\"value\": -1.3146280175338634}, {\"value\": 0.30710316801965576}, {\"value\": 0.9764680111234777}, {\"value\": 0.4821255531267423}, {\"value\": -0.6303786692328649}, {\"value\": -0.2119275801184766}, {\"value\": 0.2453884698737029}, {\"value\": 2.1194922722112217}, {\"value\": -1.0984736652517668}, {\"value\": 0.9921579694297016}, {\"value\": -0.7410914225718489}, {\"value\": 1.530756431708232}, {\"value\": 0.004909631179921292}, {\"value\": -1.7841908588507744}, {\"value\": -0.6954882806619868}, {\"value\": -0.9181771261593819}, {\"value\": 1.4827031271651419}, {\"value\": -0.7715790187209336}, {\"value\": -0.36802288462362126}, {\"value\": 0.9828537450001521}, {\"value\": 0.0740554331236376}, {\"value\": 0.23036368729885656}, {\"value\": 0.4376496173202395}, {\"value\": 0.587801167717389}, {\"value\": 1.0760193907632776}, {\"value\": -1.7232317480455905}, {\"value\": -1.7929441076230088}, {\"value\": -1.7433944170161078}, {\"value\": -0.18228737563745456}, {\"value\": -0.07940280528617301}, {\"value\": -1.4442167649649724}, {\"value\": 1.2268614676637484}, {\"value\": -2.2161781796315405}, {\"value\": 0.3818756382889422}, {\"value\": -2.569612904543444}, {\"value\": -0.003385289725143324}, {\"value\": -1.080640468192583}, {\"value\": -0.09941121983395426}, {\"value\": -0.8371699688976252}, {\"value\": 0.3002630965398346}, {\"value\": 1.0505566814047584}, {\"value\": 2.707206363383066}, {\"value\": -1.2033380407450531}, {\"value\": 1.619164048103074}, {\"value\": 0.39150917270778196}, {\"value\": -1.5996026916970392}, {\"value\": 0.1662914741949126}, {\"value\": 1.1983852743398598}, {\"value\": -1.552578481153862}, {\"value\": 0.43270203104012994}, {\"value\": 0.5555838190567748}, {\"value\": 0.3695744280992057}, {\"value\": 0.6001764577655755}, {\"value\": -0.40793253288365117}, {\"value\": 0.592367945783961}, {\"value\": 1.1085463701467537}, {\"value\": -2.120957942179976}, {\"value\": -0.059100669210179244}, {\"value\": -0.5466420144640085}, {\"value\": 0.5153263372197098}, {\"value\": -0.6607721297401306}, {\"value\": -0.44198549056058273}, {\"value\": 0.04903213082936615}, {\"value\": -0.9855151788037073}, {\"value\": -1.0781114949931956}, {\"value\": -0.37741396444139896}, {\"value\": 0.4830424738932153}, {\"value\": 0.1713956521172348}, {\"value\": 0.9693697253848033}, {\"value\": -1.7913828249372337}, {\"value\": 0.37502640275353905}, {\"value\": -0.8431615550414275}, {\"value\": -0.953644326761079}, {\"value\": 1.096892080504231}, {\"value\": -1.0264923249268318}, {\"value\": -1.7027431359052108}, {\"value\": 1.246335464289543}, {\"value\": -0.19015520179971204}, {\"value\": -0.32752249592243426}, {\"value\": 0.44210835550938965}, {\"value\": -1.0464934902161023}, {\"value\": -0.2485893291080748}, {\"value\": 0.8231874316513547}, {\"value\": 0.37107884178169565}, {\"value\": -1.8434283750898428}, {\"value\": 1.5080382350501296}, {\"value\": -0.8355350817854252}, {\"value\": -0.6812489498026647}, {\"value\": 1.4040008971529128}, {\"value\": -0.5214084025948239}, {\"value\": 0.3054275268185194}, {\"value\": -0.00026242897304575605}, {\"value\": 0.5053545640425496}, {\"value\": -1.7287735179705073}, {\"value\": -0.6187103046214608}, {\"value\": -0.27257236754445724}, {\"value\": 0.40556508291863036}, {\"value\": 1.3013449999452413}, {\"value\": 0.736512839179949}, {\"value\": -1.150702974912416}, {\"value\": -0.07526972326441664}, {\"value\": 1.4126041264703555}, {\"value\": 0.4629499922665943}, {\"value\": 0.23767499846291637}, {\"value\": 1.097632038636011}, {\"value\": 0.9633352132135995}, {\"value\": 0.792091527946276}, {\"value\": 0.19745158591715675}, {\"value\": -1.3735788313654862}, {\"value\": 0.8960587302390884}, {\"value\": -2.5564648018994998}, {\"value\": -1.4184260002364484}, {\"value\": 0.3388853418948526}, {\"value\": 1.4200926144634725}, {\"value\": -0.9005978008253127}, {\"value\": 0.6556288246447439}, {\"value\": 0.6768451700817918}, {\"value\": -0.8719624495661669}, {\"value\": 0.26219294230794304}, {\"value\": 0.5054101918009173}, {\"value\": -1.019720115951609}, {\"value\": 1.5422078560949313}, {\"value\": 0.3404759040258352}, {\"value\": 0.12748270593742217}, {\"value\": -1.089108539925747}, {\"value\": 0.6771042488922593}, {\"value\": -0.8861879893305098}, {\"value\": -1.2397180233555096}, {\"value\": -0.25077019111899057}, {\"value\": -0.06390066792285648}, {\"value\": 0.6745681868546539}, {\"value\": 0.30836719908518173}, {\"value\": 0.6334680557466532}, {\"value\": -0.5726119576313917}, {\"value\": -0.5310091651775563}, {\"value\": -1.1425547801228244}, {\"value\": -0.8557080013895683}, {\"value\": -0.611380042429657}, {\"value\": -0.7813094841978411}, {\"value\": 1.100023612528315}, {\"value\": 0.7859893770178247}, {\"value\": -1.3331176465349877}, {\"value\": -0.5747473991877319}, {\"value\": 0.3503548077268663}, {\"value\": -0.32931121496152704}, {\"value\": 0.46591009971946634}, {\"value\": -1.4922556735696932}, {\"value\": 0.774944524221936}, {\"value\": 0.0496276276721808}, {\"value\": 1.7329287484588887}, {\"value\": -1.452857652993622}, {\"value\": -0.17728623501158533}, {\"value\": -1.6593190934391597}, {\"value\": -0.2725432567784835}, {\"value\": 0.09552885134725421}, {\"value\": -1.533862640878336}, {\"value\": -0.8964194961107068}, {\"value\": 1.533691541321526}, {\"value\": -0.935299147517869}, {\"value\": 2.3198537991697146}, {\"value\": -0.22738604523041728}, {\"value\": -0.3448186366503107}, {\"value\": -0.18540036308802027}, {\"value\": 0.41639095280812505}, {\"value\": -0.050587260889951795}, {\"value\": 0.18055106508326796}, {\"value\": -1.0662640562775285}, {\"value\": -1.5992065058673064}, {\"value\": 0.31500195945455983}, {\"value\": 0.18184186921734863}, {\"value\": 0.21512214136513677}, {\"value\": 1.3571375029432158}, {\"value\": 1.2350056342408544}, {\"value\": -0.4080645160270434}, {\"value\": -0.1031934865441145}, {\"value\": 1.0407001803588956}, {\"value\": -1.7595242169058067}, {\"value\": -1.4810019986378058}, {\"value\": -0.3121234603551977}, {\"value\": 1.4693053843465407}, {\"value\": 1.413548721561444}, {\"value\": 1.8273309808162475}, {\"value\": 1.2134188507333765}, {\"value\": 0.914925287359246}, {\"value\": -1.488851830172118}, {\"value\": 0.9571623335661961}, {\"value\": 0.1822678780891102}, {\"value\": -0.8451242359799209}, {\"value\": -0.5093831718777171}, {\"value\": 0.638830914125397}, {\"value\": 0.05401830758561086}, {\"value\": -0.6200184748164063}, {\"value\": 0.9371442624354405}, {\"value\": 1.3467910699416015}, {\"value\": -1.1583282930884722}, {\"value\": 0.4197069729009851}, {\"value\": 0.23903557180368196}, {\"value\": 0.129430693731493}, {\"value\": -0.6079997679086747}, {\"value\": 0.005207480107852433}, {\"value\": 0.9211961606888855}, {\"value\": -0.7120033952314465}, {\"value\": -1.0074537470418756}, {\"value\": -0.9367096317387441}, {\"value\": -0.48762017303384775}, {\"value\": 0.6846543537234038}, {\"value\": -1.2021420494124886}, {\"value\": -0.3739635049411543}, {\"value\": -1.5885313544569284}, {\"value\": 0.6465042236301808}, {\"value\": -0.14823609030083243}, {\"value\": -2.1101461520798277}, {\"value\": -1.1126409788438858}, {\"value\": -0.7061546130058215}, {\"value\": 0.5734411030205501}, {\"value\": 2.1088303570789213}, {\"value\": 0.03634563322752306}, {\"value\": -0.9813614433569667}, {\"value\": 0.5123848192077255}, {\"value\": -0.8225097664826303}, {\"value\": 0.7166137142883243}, {\"value\": 1.8675765506679953}, {\"value\": -0.26543641959585146}, {\"value\": -0.024229532156396623}, {\"value\": -1.1463661512308383}, {\"value\": -1.7282580124276008}, {\"value\": -0.11382502798868013}, {\"value\": 0.39786741901090183}, {\"value\": 0.2565038469466288}, {\"value\": 0.9623091775134691}, {\"value\": -0.8416348935271311}, {\"value\": -0.2927103264721879}, {\"value\": 0.46741752308048484}, {\"value\": -0.8778049649604891}, {\"value\": 0.945064393789735}, {\"value\": 0.054131464533704744}, {\"value\": -0.21442525688141742}, {\"value\": 0.05698534800244074}, {\"value\": 0.8592089864806759}, {\"value\": 2.106243047870297}, {\"value\": 0.4368218639704444}, {\"value\": -0.8384568707703834}, {\"value\": -0.6205831947779761}, {\"value\": -2.2770215244644234}, {\"value\": 0.24465303016628268}, {\"value\": 0.3179032201816417}, {\"value\": -1.2776565869111594}, {\"value\": 0.3946476467757193}, {\"value\": 0.9110576776224367}, {\"value\": -0.2574040742826267}, {\"value\": -1.9117639550667402}, {\"value\": 0.7378168212259602}, {\"value\": -1.483549512938965}, {\"value\": 2.3594610222364802}, {\"value\": -0.9295858357578278}, {\"value\": 0.06885635973535081}, {\"value\": -1.507411951778774}, {\"value\": 0.7214004971455603}, {\"value\": -1.0868854438034268}, {\"value\": -2.5051957569842416}, {\"value\": 1.2131727282279794}, {\"value\": -0.37315481970256703}, {\"value\": -1.131524220718981}, {\"value\": 1.110243316642922}, {\"value\": 0.07310940034353967}, {\"value\": 0.7191911669585239}, {\"value\": -1.1932294348663013}, {\"value\": -0.9930124302581947}, {\"value\": -0.8519244225912186}, {\"value\": 0.9258948124635298}, {\"value\": -0.9483878492620277}, {\"value\": -0.7906229674285398}, {\"value\": 0.7981590627516311}, {\"value\": 0.6967928701169402}, {\"value\": -3.004511192122877}, {\"value\": 0.05594431905003099}, {\"value\": 0.914793968287613}, {\"value\": 0.2310429815236812}, {\"value\": 0.43292754360787705}, {\"value\": 1.015695912300883}, {\"value\": -1.085707523834637}, {\"value\": 0.31708135973505025}, {\"value\": -0.11022124325235236}, {\"value\": 1.203429065158237}, {\"value\": 0.970616360364432}, {\"value\": -0.7194370233523866}, {\"value\": -0.1309764581266377}, {\"value\": 0.8764013321399501}, {\"value\": 0.5334961575491296}, {\"value\": -0.40173665652716545}, {\"value\": 0.8055581013115773}, {\"value\": -0.40850604502581267}, {\"value\": 0.21434243520984803}, {\"value\": -0.9768664564272843}, {\"value\": 1.2443459297620036}, {\"value\": 0.032879834517027924}, {\"value\": 0.4941488260115539}, {\"value\": -0.4409435803269429}, {\"value\": 0.43860610493504226}, {\"value\": 0.6298221437762888}, {\"value\": -0.08766855872853078}, {\"value\": -1.2608467499385634}, {\"value\": -1.0655193173951651}, {\"value\": -0.44868079088605944}, {\"value\": 0.057796517433956605}, {\"value\": 0.41210025834002495}, {\"value\": -0.22863109725989608}, {\"value\": -0.9798675331744015}, {\"value\": -0.5236739394311868}, {\"value\": 0.009447833434963708}, {\"value\": -1.151061447114845}, {\"value\": -0.7935471740769038}, {\"value\": 1.5828966596123435}, {\"value\": 0.41337825609915746}, {\"value\": -0.40259807670111325}, {\"value\": -0.023786151087183936}, {\"value\": -0.9697737920859056}, {\"value\": -0.6503766318621023}, {\"value\": -0.8144364079620048}, {\"value\": -1.2653674584932426}, {\"value\": 0.04708617434400949}, {\"value\": 0.24263696078923952}, {\"value\": 0.766060677758481}, {\"value\": -0.832980883005306}, {\"value\": 2.207602270358448}, {\"value\": -0.3420127323887241}, {\"value\": 1.2612712607959418}, {\"value\": -0.8169952021359994}, {\"value\": 0.014800962212783137}, {\"value\": 1.58350409398664}, {\"value\": 0.1845919115564005}, {\"value\": -1.6658803755626006}, {\"value\": 0.2573290370604603}, {\"value\": 0.10632923771021846}, {\"value\": -1.8220826738923974}, {\"value\": -0.9257199707354898}, {\"value\": -0.30335852661077006}, {\"value\": -1.7877994252550267}, {\"value\": 0.3522575830401256}, {\"value\": 2.058049720848919}, {\"value\": 0.7878181889679001}, {\"value\": -0.4506771024235582}, {\"value\": -0.8005652715853504}, {\"value\": -2.3827517218643353}, {\"value\": 0.8167698772121048}, {\"value\": -0.2829273758082332}, {\"value\": 1.8220265056690528}, {\"value\": -0.5708709987774578}, {\"value\": -2.589579708147511}, {\"value\": 0.2923405069158074}, {\"value\": 1.2758954542501584}, {\"value\": 0.9340701889305987}, {\"value\": 0.46640064681132526}, {\"value\": 0.39285177514363695}, {\"value\": 0.1934826219007142}, {\"value\": 1.575212686434062}, {\"value\": 0.8197898074113055}, {\"value\": 0.5202168646407597}, {\"value\": -1.266517769383786}, {\"value\": -0.6837575493234329}, {\"value\": -0.5797672045840405}, {\"value\": 1.4363548050296449}, {\"value\": 0.9689304514883892}, {\"value\": 0.9881491128653638}, {\"value\": -0.3415802282900164}, {\"value\": -0.07359725174193936}, {\"value\": 0.8623327389239341}, {\"value\": 1.5740558291567264}, {\"value\": -1.1165970771295914}, {\"value\": 0.7832733791849807}, {\"value\": -0.9539811313084255}, {\"value\": 0.8056761979451716}, {\"value\": 1.1504483535145194}, {\"value\": 0.33164165021308273}, {\"value\": -0.5938001487554605}, {\"value\": -1.371251240037739}, {\"value\": 1.264026483421907}, {\"value\": 0.3920969451430625}, {\"value\": 0.5987991051826786}, {\"value\": 0.023745720235055716}, {\"value\": 2.166896679527975}, {\"value\": 0.34894865262896857}, {\"value\": 0.09344192184370788}, {\"value\": -0.9752974534513312}, {\"value\": 3.0323283940506864}, {\"value\": 1.457917194986317}, {\"value\": -1.5911424130008132}, {\"value\": -0.4867883123679297}, {\"value\": 0.1401338884685496}, {\"value\": 0.31389662070252194}, {\"value\": 0.2665180774860569}, {\"value\": 0.6522976408821161}, {\"value\": 0.24694297278328603}, {\"value\": 0.29398902230591073}, {\"value\": 0.9516162370340391}, {\"value\": -1.06845042324349}, {\"value\": 0.972576695048878}, {\"value\": 0.5436295223039299}, {\"value\": -0.8050419219060037}, {\"value\": -1.825434964341959}, {\"value\": 1.147844594786281}, {\"value\": 1.3023336476122753}, {\"value\": -0.6935082845645386}, {\"value\": 0.07397116178580374}, {\"value\": 0.7917548972848812}, {\"value\": -0.5291005033762758}, {\"value\": 1.3200957722774262}, {\"value\": 0.18463594645029324}, {\"value\": -0.6440842014881467}, {\"value\": -0.26808273768126795}, {\"value\": 1.0190149114705145}, {\"value\": 1.044259477259775}, {\"value\": -0.7300782145049504}, {\"value\": -2.2890624909934694}, {\"value\": -1.3824781559998311}, {\"value\": -0.08100525786058375}, {\"value\": -1.036812888227752}, {\"value\": -1.3427239571973029}, {\"value\": -1.1311994001417556}, {\"value\": 0.8713297501672589}, {\"value\": 0.08446215179354277}, {\"value\": 0.5487627645408587}, {\"value\": 0.5943530936661122}, {\"value\": 0.08755945409183395}, {\"value\": 1.2117112673187707}, {\"value\": 0.6511487993860499}, {\"value\": 0.07277266288850692}, {\"value\": 0.4217065430990948}, {\"value\": 1.7776622069535863}, {\"value\": 1.451606831060396}, {\"value\": -1.1266752645714355}, {\"value\": 1.1302389338721621}, {\"value\": 0.14682775465927195}, {\"value\": -1.7599470691537904}, {\"value\": -1.6305134161494546}, {\"value\": 0.7676141904072047}, {\"value\": 0.5257733574052527}, {\"value\": 2.1388692131144027}, {\"value\": -0.07156845961081368}, {\"value\": -2.854825089170744}, {\"value\": 1.1598602613572186}, {\"value\": 2.2715103761687323}, {\"value\": -0.3824708540984448}, {\"value\": -0.5546135510208332}, {\"value\": -0.2761416132778232}, {\"value\": -0.26407664440977663}, {\"value\": 1.6216153350154017}, {\"value\": -1.7509328201777503}, {\"value\": 0.5412409330771684}, {\"value\": 2.191951299106625}, {\"value\": 1.2087918962956292}, {\"value\": -0.4622478053971226}, {\"value\": -0.29425251066700225}, {\"value\": -0.5705206335222897}, {\"value\": 0.2095968773187579}, {\"value\": 0.118409378848471}, {\"value\": -0.6391060858816728}, {\"value\": 0.6195368830470089}, {\"value\": 0.4272786479243286}, {\"value\": 1.5194578237898513}, {\"value\": 0.8658737441918534}, {\"value\": 0.5440485042100199}, {\"value\": -0.2436444159751085}, {\"value\": -0.5021733634169164}, {\"value\": 0.6701484303100066}, {\"value\": -0.6526630722094504}, {\"value\": -0.04211968870656844}, {\"value\": -1.7435168999526345}, {\"value\": 1.3969825600094241}, {\"value\": -1.1616483298692937}, {\"value\": 0.8712814985820447}, {\"value\": 0.3299633203286959}, {\"value\": -0.9954589784032952}, {\"value\": -0.8455942230575846}, {\"value\": 1.121595182942279}, {\"value\": 0.4903018948582818}, {\"value\": -1.1615317853528582}, {\"value\": -0.4533873351759578}, {\"value\": 0.977683237670669}, {\"value\": -1.0714385687366466}, {\"value\": 0.12663469113407397}, {\"value\": 0.12106349266524559}, {\"value\": 0.40859102858952123}, {\"value\": -0.5755081381889997}, {\"value\": 0.5686658645298507}, {\"value\": -0.5616272659556105}, {\"value\": 0.02608493926306789}, {\"value\": -0.9410762464134315}, {\"value\": -0.6520366113368541}, {\"value\": 1.6765355858144098}, {\"value\": 0.14586524466457737}, {\"value\": 0.5315563892122245}, {\"value\": 0.7472295614487088}, {\"value\": -0.05297715234438794}, {\"value\": -0.05297496426809962}, {\"value\": 0.5752218335185074}, {\"value\": -1.4479669702579783}, {\"value\": -0.9006908333888939}, {\"value\": 0.19220506970738163}, {\"value\": -0.5589765333986246}, {\"value\": -0.1160460701596056}, {\"value\": -1.7517276767847234}, {\"value\": -0.8392530675209806}, {\"value\": -0.13399116707885936}, {\"value\": -0.08250286028400332}, {\"value\": -0.348129645052686}, {\"value\": -0.8927377037101799}, {\"value\": -0.16004879973491093}, {\"value\": 1.0873167604972556}, {\"value\": -0.20123741214935914}, {\"value\": -0.004425817412180332}, {\"value\": 1.038128084660317}, {\"value\": -0.15732180555117223}, {\"value\": 0.34299514455264185}, {\"value\": 1.0773303865891375}, {\"value\": -0.019331726475682615}, {\"value\": 1.3941883970171784}, {\"value\": 0.5127399433920085}, {\"value\": 1.1144939867156016}, {\"value\": 1.4500966371248236}, {\"value\": -0.1075067664235944}, {\"value\": 0.4957486938484909}, {\"value\": 0.9245318192912079}, {\"value\": -1.1762279746321092}, {\"value\": 1.1580172383908975}, {\"value\": 1.1920621245733276}, {\"value\": -0.9461992588499282}, {\"value\": -1.2068729853700875}, {\"value\": -0.08455089293301637}, {\"value\": -0.6955601571423974}, {\"value\": -1.2280239014908698}, {\"value\": -0.6014067948546499}, {\"value\": 2.3084023003668985}, {\"value\": 0.00015311395523961695}, {\"value\": 0.3467074313001787}, {\"value\": 0.06823721823261557}, {\"value\": 0.3352921554827234}, {\"value\": 1.246997347867213}, {\"value\": 0.0098975242962245}, {\"value\": 0.7782805304016014}, {\"value\": 1.2098338854327086}, {\"value\": -0.7104043130236717}, {\"value\": 0.555717818457262}, {\"value\": 1.2442841120831718}, {\"value\": 0.00779155037297698}, {\"value\": 1.4590956081992448}, {\"value\": 0.050265546284847626}, {\"value\": -0.7573987459285784}, {\"value\": -2.040800415006217}, {\"value\": -0.9632353318628671}, {\"value\": 0.18108798760775807}, {\"value\": -0.5632083623565763}, {\"value\": -0.41406819383383486}, {\"value\": -1.0321506105594882}, {\"value\": 1.2701700694828801}, {\"value\": 0.260919662747026}, {\"value\": 0.7539881955368001}, {\"value\": 0.9509209550807082}, {\"value\": -0.10559239257643661}, {\"value\": -1.101632242043174}, {\"value\": 0.8251444818441336}, {\"value\": -0.41741395526821373}, {\"value\": -0.24228230782111282}, {\"value\": 0.5816463208531627}, {\"value\": -0.9531849177950765}, {\"value\": -0.379314269276095}, {\"value\": 0.3875224479111914}, {\"value\": 0.0935254159702829}, {\"value\": 0.7083906717795213}, {\"value\": 1.7118267685006427}, {\"value\": 0.5085637213579353}, {\"value\": 2.2643398397318584}, {\"value\": -1.2980788985248104}, {\"value\": 0.1722895775307414}, {\"value\": -0.7901978526302877}, {\"value\": 0.7134937718945895}, {\"value\": -0.27978708524354795}, {\"value\": 1.1856709565829302}, {\"value\": 1.5373291718229019}, {\"value\": 2.0467365401211723}, {\"value\": 0.13481604162211902}, {\"value\": 0.3097769937965486}, {\"value\": -0.2531846078703833}, {\"value\": 0.9959319781642951}, {\"value\": -0.9870875554463772}, {\"value\": -0.11092926850152038}, {\"value\": 0.47258901320405433}, {\"value\": 0.7462692679547998}, {\"value\": -0.20522378883179423}, {\"value\": -0.15327209181823204}, {\"value\": 0.7094007593232058}, {\"value\": 0.1852911684108972}, {\"value\": 1.0702148011389594}, {\"value\": 1.1639933388079429}, {\"value\": -0.47071470360154566}, {\"value\": 1.008269306696245}, {\"value\": 0.8476081503091002}, {\"value\": 0.6504133078522907}, {\"value\": 0.15173209967297005}, {\"value\": -0.1508475973786209}, {\"value\": 1.2380055768733746}, {\"value\": -2.18866807031378}, {\"value\": 0.5996555137569922}, {\"value\": 0.5656940326189195}, {\"value\": -0.3578095328670627}, {\"value\": 1.2614496433120657}, {\"value\": -0.1115953264498727}, {\"value\": -0.8311330817801008}, {\"value\": -1.5475921548762126}, {\"value\": 1.5283091307347907}, {\"value\": 1.126718171012733}, {\"value\": -0.3192331332932739}, {\"value\": -1.2318014248884763}, {\"value\": 0.5407924851493222}, {\"value\": 0.08538081610494075}, {\"value\": -1.9553335785507742}, {\"value\": 0.07813673333694149}, {\"value\": -2.375976328299113}, {\"value\": 0.9284269684328578}, {\"value\": 2.232380239614197}, {\"value\": -0.182024879728832}, {\"value\": -0.9732951789685641}, {\"value\": 1.0023221881255435}, {\"value\": -1.1317454388735066}, {\"value\": 0.2389234991546862}, {\"value\": 1.2089847699131653}, {\"value\": -0.3982582775479919}, {\"value\": 1.8393350181265322}, {\"value\": -1.0549590017600787}, {\"value\": -1.8541545123726424}, {\"value\": -2.046236099452725}, {\"value\": -0.8343477163849338}, {\"value\": 0.8277766744086902}, {\"value\": -0.4143635862938575}, {\"value\": -0.5486247091650216}, {\"value\": -1.2887289702720706}, {\"value\": 0.10405661561491894}, {\"value\": -0.20569776556193306}, {\"value\": -0.47371823569506427}, {\"value\": 1.745609589245756}, {\"value\": -0.435098669096508}, {\"value\": -0.3152639911690705}, {\"value\": -0.46224434589377705}, {\"value\": 0.5065143691661629}, {\"value\": 0.11632284462180814}, {\"value\": -1.6375167504186159}, {\"value\": -0.8058842896336365}, {\"value\": 0.022502970412604236}, {\"value\": -1.5648825339405201}, {\"value\": 1.0844682889259845}, {\"value\": -0.43597812080154286}, {\"value\": 0.31873212788246535}, {\"value\": 0.5689353335849343}, {\"value\": 1.0658835162944214}, {\"value\": 0.22323256188453092}, {\"value\": 0.6075004520708763}, {\"value\": -0.5992415638081267}, {\"value\": 0.4132568248198025}, {\"value\": 0.05808224521480838}, {\"value\": -0.9549065973135542}, {\"value\": 0.24232810031842603}, {\"value\": -1.8952018813358926}, {\"value\": 1.7564609691935729}, {\"value\": 0.19702076784475075}, {\"value\": 1.2892385167778933}, {\"value\": 0.29658650599756964}, {\"value\": 0.3020472123712642}, {\"value\": 0.17874544621222427}, {\"value\": -0.4565221165608606}, {\"value\": 0.7191084504777349}, {\"value\": 0.6182894347985918}, {\"value\": -0.7927538052478925}, {\"value\": -0.48005176127561466}, {\"value\": 0.684026820247713}, {\"value\": -0.7818977610887696}, {\"value\": -0.20598384320199822}, {\"value\": -0.182868440729382}, {\"value\": -0.415860270765357}, {\"value\": -0.9965861502310043}, {\"value\": -1.381695278246342}, {\"value\": -1.4273068496957477}, {\"value\": -1.6124039009797877}, {\"value\": -0.7874513704859001}, {\"value\": 1.2929195282861066}, {\"value\": -1.3978033024833572}, {\"value\": 1.3901824198895176}, {\"value\": -2.014997065762533}, {\"value\": 2.317821074871185}, {\"value\": 0.9336929633494594}, {\"value\": 0.8809498105176152}, {\"value\": -0.671143205997284}, {\"value\": -1.248670529398229}, {\"value\": -4.144038504509087}, {\"value\": -0.030434326261572064}, {\"value\": 0.011191585175022563}, {\"value\": 1.4984749740706675}, {\"value\": -0.6578558284922387}, {\"value\": -0.12565144837156855}, {\"value\": -0.5770052462404304}, {\"value\": -0.7441547225414991}, {\"value\": -0.7471182612341947}, {\"value\": 0.8583093172431471}, {\"value\": -0.9845226721174346}, {\"value\": -1.5234198046563976}, {\"value\": 0.42805410391433324}, {\"value\": -0.196818795489281}, {\"value\": -0.9824177543293358}, {\"value\": 0.3418496323071321}, {\"value\": -0.05788747958255726}, {\"value\": -0.2715223544668242}, {\"value\": 1.2598442567333998}, {\"value\": -0.3075944842277705}, {\"value\": 0.7019966576252209}, {\"value\": 1.2672957220916614}, {\"value\": -0.588574660190779}, {\"value\": -0.687958174905827}, {\"value\": -1.864907482806721}, {\"value\": -0.6749255827235447}, {\"value\": -0.8120142014292375}, {\"value\": -1.6697955859813314}, {\"value\": 0.22928986837657572}, {\"value\": -0.5485966250794327}, {\"value\": -0.3582946368926604}, {\"value\": -1.6028090979162728}, {\"value\": 0.6469300333865675}, {\"value\": -1.4765040921629122}, {\"value\": 0.2003684134228597}, {\"value\": 2.0967550143941165}, {\"value\": -0.820886018731583}, {\"value\": 0.012910452257378607}, {\"value\": 1.1191799626034327}, {\"value\": -2.775702526152739}, {\"value\": 0.04407992580219176}, {\"value\": -0.6346476644264278}, {\"value\": 0.8491969278188192}, {\"value\": 0.5050565658273437}, {\"value\": -0.6461035126096158}, {\"value\": 0.46234182347991776}, {\"value\": 0.9215676147801551}, {\"value\": -0.7003409703076234}, {\"value\": 1.461810152869294}, {\"value\": -1.9235386849232583}, {\"value\": 2.926144291861876}, {\"value\": -0.19540747656699298}, {\"value\": 0.7989835953053724}, {\"value\": -0.3803421534189744}, {\"value\": 1.919763874074482}, {\"value\": -0.46009715568487364}, {\"value\": 0.5520768784527907}, {\"value\": 1.1283123756630233}, {\"value\": -1.502878684697101}, {\"value\": 0.6482875556224807}, {\"value\": 0.381708616673751}, {\"value\": 0.4706508895760836}, {\"value\": 0.1346473527387988}, {\"value\": 1.2247391971030959}, {\"value\": 0.7520826609901304}, {\"value\": 0.06874413338197169}, {\"value\": 0.07302389950168778}, {\"value\": -2.263599590009943}, {\"value\": -2.275688042244345}, {\"value\": -0.4910932452427411}, {\"value\": 0.71291639664712}, {\"value\": 0.31651846063217565}, {\"value\": -0.32262700559120183}, {\"value\": 0.304565275109561}, {\"value\": 0.7001177103892606}, {\"value\": 0.833727006683383}, {\"value\": -0.4371909260274297}, {\"value\": 0.9315902003674812}, {\"value\": -0.39112244954358927}, {\"value\": -1.2987789045960554}, {\"value\": 0.8763629845382497}, {\"value\": -0.1665952437877033}, {\"value\": -1.3405432648826645}, {\"value\": -0.22839979363879662}, {\"value\": -0.21943452630398225}, {\"value\": 1.6107404805805872}, {\"value\": -0.6019657980045878}, {\"value\": 0.7213192800325585}, {\"value\": -1.2302349576140879}, {\"value\": 0.8531068360129608}, {\"value\": -0.6765951907930787}, {\"value\": -1.764851651703974}, {\"value\": 0.9002297026361428}, {\"value\": -1.059963265372538}, {\"value\": 0.5215292679220107}, {\"value\": 0.8704759007961579}, {\"value\": -1.7064716816126109}, {\"value\": 0.7437211096501143}, {\"value\": 0.3671537494335212}, {\"value\": -0.11579425325068057}, {\"value\": -0.481380859545923}, {\"value\": 2.2206313248117437}, {\"value\": -0.15120311174606968}, {\"value\": 1.7350223093224337}, {\"value\": 0.646464456421285}, {\"value\": -0.9980371333298099}, {\"value\": -0.05221809022273946}, {\"value\": 0.2635803888884288}, {\"value\": 0.02326408466750899}, {\"value\": -0.5437850530091352}, {\"value\": -0.024448754636961702}, {\"value\": 0.09155222612123584}, {\"value\": -0.19374378879988718}, {\"value\": -0.7846482558823891}, {\"value\": -0.08864660855871108}, {\"value\": 0.14874921981080252}, {\"value\": 2.055311621065097}, {\"value\": 0.22879847113604135}, {\"value\": 0.3364704038546846}, {\"value\": 1.15681085982932}, {\"value\": -0.34721156991086}, {\"value\": 0.0011372307111307501}, {\"value\": -1.3458989646702173}, {\"value\": 1.2212136209986362}, {\"value\": -0.9728051239975779}, {\"value\": 0.060809008625829525}, {\"value\": -1.510689487310551}, {\"value\": 1.2234884939441504}, {\"value\": 0.4365219991729702}, {\"value\": -2.1874780471127826}, {\"value\": -1.073004571439592}, {\"value\": -0.869333560964887}, {\"value\": 0.566583750900843}, {\"value\": 2.1041004301303525}, {\"value\": -0.4967146466299798}, {\"value\": -0.3614644819109555}, {\"value\": -0.3119283802577143}, {\"value\": -0.3081682356913591}, {\"value\": 0.21631851144903252}, {\"value\": -0.10784062582184328}, {\"value\": -1.198356418741394}, {\"value\": -0.6769387808604479}, {\"value\": -0.1180114576994931}, {\"value\": 2.247968420849226}, {\"value\": -0.9443837097406137}, {\"value\": -1.4340524639377616}, {\"value\": 1.1903748316756857}, {\"value\": 0.3588727473028671}, {\"value\": -0.4752314842338477}, {\"value\": -0.4447784213443077}, {\"value\": -0.6401880072240291}, {\"value\": 0.427160009284807}, {\"value\": -1.3051605956998853}, {\"value\": 0.3195960841740743}, {\"value\": -0.4518503563145978}, {\"value\": 1.7111216769435775}, {\"value\": 0.9251713238911529}, {\"value\": 0.4709385821760249}, {\"value\": 0.7934905551608843}, {\"value\": -0.7467094807046856}, {\"value\": 0.08930958729624655}, {\"value\": -0.9597105847851952}, {\"value\": 1.139694214095506}, {\"value\": -0.2360028583255979}, {\"value\": -0.11951175269866442}, {\"value\": -2.565661875503577}, {\"value\": -1.1501411375816049}, {\"value\": 0.8938125977491648}, {\"value\": -0.7355178104118846}, {\"value\": 0.9265951684801101}, {\"value\": -0.6402885245747085}, {\"value\": -1.1365247583889184}, {\"value\": -0.3297788005869573}, {\"value\": 0.0785649771655424}, {\"value\": -0.5272589426562754}, {\"value\": 2.086257904938789}, {\"value\": -0.24109530370035015}, {\"value\": -0.39400287745425144}, {\"value\": 0.8265913417334226}, {\"value\": 1.2009603081362563}, {\"value\": -0.10702792357497257}, {\"value\": 1.6164726956837316}, {\"value\": -1.1648636316652514}, {\"value\": 0.1880991462525072}, {\"value\": 0.9041986859220144}, {\"value\": 0.2006046908837759}, {\"value\": 0.45967073467256747}, {\"value\": 0.8377267299918716}, {\"value\": -1.6377182830321473}, {\"value\": -0.5137292460279395}, {\"value\": -0.33849692375724266}, {\"value\": -0.21181752629355036}, {\"value\": -0.5143937732017326}, {\"value\": 0.8526681960511574}, {\"value\": 0.8200331614651827}, {\"value\": 1.050700082817515}, {\"value\": 1.0741496722449009}, {\"value\": 0.49020436871764866}, {\"value\": 1.508606686440121}, {\"value\": 0.06271735257827665}, {\"value\": 0.5068111246148841}, {\"value\": -0.07184689995769539}, {\"value\": -0.04836525542228165}, {\"value\": 0.6190199463717981}, {\"value\": -1.7556567744424174}, {\"value\": -0.20365171335073134}, {\"value\": 1.1067596627677123}, {\"value\": -1.476397889176135}, {\"value\": -0.3506336396833704}, {\"value\": -1.175722001985303}, {\"value\": -2.861648393325436}, {\"value\": -1.060416690864524}, {\"value\": 0.5638045511114161}, {\"value\": 0.2144794310766872}, {\"value\": -0.6160257931862423}, {\"value\": -0.19242501457163555}, {\"value\": -0.4351907976850194}, {\"value\": 0.045255015075398454}, {\"value\": -0.404263544960922}, {\"value\": 0.2849981309718422}, {\"value\": 1.39749550244588}, {\"value\": -1.226842021031629}, {\"value\": -0.6871788274319091}, {\"value\": -0.2541562528073459}, {\"value\": 0.794780774764497}, {\"value\": -0.8004391445475721}, {\"value\": -0.9403440921731158}, {\"value\": -0.4695916467433186}, {\"value\": -1.041048720868488}, {\"value\": -1.5804762352616697}, {\"value\": -0.686174718147045}, {\"value\": -0.9394547084089897}, {\"value\": -0.5453580765103933}, {\"value\": -1.0036633970750217}, {\"value\": 0.09449486186884017}, {\"value\": 1.4594036776598274}, {\"value\": 0.339894428314149}, {\"value\": -1.326349986663386}, {\"value\": 0.1666649246108152}, {\"value\": -1.2900753687114936}, {\"value\": -0.489518101867029}, {\"value\": 0.9309348239424403}, {\"value\": -1.4121182409427142}, {\"value\": -0.23557513759638013}, {\"value\": 1.6007077473394078}, {\"value\": 1.8434770394922975}, {\"value\": -0.6521982259642747}, {\"value\": -0.32269963089768916}, {\"value\": 0.554991523775207}, {\"value\": 0.880152078661037}, {\"value\": 0.5577609313449258}, {\"value\": -0.6566122237498233}, {\"value\": 0.7247865626152109}, {\"value\": -1.4028186587541809}, {\"value\": -0.8233597545759044}, {\"value\": 0.8266321065585992}, {\"value\": 0.9090707324916412}, {\"value\": -0.5876593761295411}, {\"value\": -0.08571348469415875}, {\"value\": -1.5113923828907574}, {\"value\": -0.8563498007007027}, {\"value\": 1.6953490942148561}, {\"value\": -1.05690273581257}, {\"value\": -0.19496056582039484}, {\"value\": -2.0381839080565274}, {\"value\": -0.9331381376320736}, {\"value\": 0.08006012884576941}, {\"value\": 0.4219460115837428}, {\"value\": 0.6837139404951286}, {\"value\": 0.9524350849801657}, {\"value\": -0.8489940085286098}, {\"value\": 0.028634941202835443}, {\"value\": -0.10523244486952056}, {\"value\": 1.192392076335711}, {\"value\": -0.741211971161322}, {\"value\": -0.49267019089234876}, {\"value\": -0.7417463048682578}, {\"value\": -0.45051181579729227}, {\"value\": -1.3657429440805666}, {\"value\": 0.0892981968807277}, {\"value\": 1.250499444229469}, {\"value\": 0.21777763500351077}, {\"value\": -1.665278637336087}, {\"value\": 0.3083803789234993}, {\"value\": -0.5781265329589688}, {\"value\": 0.15247895317344604}, {\"value\": 2.0402375389976912}, {\"value\": 0.5560264097324203}, {\"value\": 1.0208997310586896}, {\"value\": 0.8205005455041969}, {\"value\": -0.11610972708396661}, {\"value\": -0.2270246171828762}, {\"value\": -1.2567101365655158}, {\"value\": 1.1920155818820715}, {\"value\": -1.0219470657715548}, {\"value\": -0.8612759610280606}, {\"value\": 0.6957483399106056}, {\"value\": 0.2964973141848904}, {\"value\": -0.49233089105336064}, {\"value\": 0.14117740625796776}, {\"value\": 1.711139221614164}, {\"value\": 0.7843503919582243}, {\"value\": -1.285587265891129}, {\"value\": -0.35056879597231627}, {\"value\": 0.2627751756687855}, {\"value\": 0.0021126676336545584}, {\"value\": 0.42992845349041786}, {\"value\": 1.0302925044137723}, {\"value\": -2.598682087437419}, {\"value\": 0.9467244719320832}, {\"value\": -0.41878107886170207}, {\"value\": 0.5745954885097098}, {\"value\": 1.9034559009831613}, {\"value\": 0.36861937219896435}, {\"value\": -0.6117243733175235}, {\"value\": 0.8173525059939256}, {\"value\": 0.8979011669170163}, {\"value\": 1.220590140873644}, {\"value\": 2.2363013182821803}, {\"value\": 0.27758034427872785}, {\"value\": -1.7528320213290665}, {\"value\": -2.2594318962426057}, {\"value\": -1.3644179646290426}, {\"value\": 0.3369737038973887}, {\"value\": 0.07044102269243353}, {\"value\": -0.6262633778009351}, {\"value\": 0.4044621316029556}, {\"value\": 0.20511181575792709}, {\"value\": -0.7073109693755616}, {\"value\": 0.22866242662205252}, {\"value\": 0.17354563268496115}, {\"value\": 0.4726136242448865}, {\"value\": -0.09150696846436447}, {\"value\": 0.4342525574308671}, {\"value\": 0.7289529365038943}, {\"value\": 0.7255037575810999}, {\"value\": -0.81699585750244}, {\"value\": -1.039141630207717}, {\"value\": -0.2618480310028681}, {\"value\": 1.0933624296612294}, {\"value\": 0.3203856872826699}, {\"value\": -1.9430453059668802}, {\"value\": 0.3554080118723178}, {\"value\": 0.5096030118662785}, {\"value\": 0.42786998660189685}, {\"value\": 0.3626920999435554}, {\"value\": -0.48073508334195353}, {\"value\": 0.3745240165756617}, {\"value\": -0.35134658164581006}, {\"value\": 0.8764878065318583}, {\"value\": 0.45044563657142517}, {\"value\": 0.5001436212935957}, {\"value\": 1.6980287797793672}, {\"value\": -0.4761408465878703}, {\"value\": 0.4133839602953714}, {\"value\": -0.5350395693238064}, {\"value\": 0.3188346725355861}, {\"value\": -0.8006185297301194}, {\"value\": 0.761210286616747}, {\"value\": -0.29454802007914105}, {\"value\": 2.008427726837757}, {\"value\": -0.33100389830222354}, {\"value\": -0.8005980876349204}, {\"value\": 0.7823425109162332}, {\"value\": -0.739826202733439}, {\"value\": -2.1197807158146453}, {\"value\": -0.8557190272343198}, {\"value\": 1.3311287392288105}, {\"value\": 0.20137745906913296}, {\"value\": -1.1758448079123858}, {\"value\": -0.09302009174259665}, {\"value\": -0.03101066663855103}, {\"value\": -0.28431681702114026}, {\"value\": -0.22944499563044404}, {\"value\": 0.23257674876864567}, {\"value\": 0.2871091796828351}, {\"value\": -0.1401502122399754}, {\"value\": 0.8893071022415331}, {\"value\": 1.274276640154578}, {\"value\": 0.6218956333854715}, {\"value\": 0.14877490223856174}, {\"value\": -0.15661647578106433}, {\"value\": 0.8953040495712997}, {\"value\": 0.2535713279774458}, {\"value\": -0.2865937010860838}, {\"value\": -0.6180634595558572}, {\"value\": 0.8495488945357424}, {\"value\": 0.9324215384025355}, {\"value\": -0.5776116630364861}, {\"value\": 0.696425963737144}, {\"value\": 0.04172639292983165}, {\"value\": -0.532374737363672}, {\"value\": 1.0638073494166875}, {\"value\": -0.31078345846685396}, {\"value\": -1.542146756026075}, {\"value\": 0.9661394889461001}, {\"value\": -0.8177282003457051}, {\"value\": 0.894347325775303}, {\"value\": 0.806875254324466}, {\"value\": 0.20032588081819092}, {\"value\": -0.9179720620504382}, {\"value\": -1.05422674407432}, {\"value\": -0.07373479042199826}, {\"value\": -1.200154053268466}, {\"value\": -0.09661311512573324}, {\"value\": 0.19444090461515434}, {\"value\": 0.5123214374441388}, {\"value\": 1.0524573108560913}, {\"value\": 0.6607719913672845}, {\"value\": -1.5316330912953737}, {\"value\": 0.23406999621879018}, {\"value\": -0.3583121026348971}, {\"value\": 0.8241372307404405}, {\"value\": 0.6570180054685362}, {\"value\": 0.22411726732355775}, {\"value\": 0.3304911967696774}, {\"value\": -1.1581210702484632}, {\"value\": -0.11278180496979154}, {\"value\": 1.129788976014987}, {\"value\": 0.10999664163732441}, {\"value\": -1.055774076024701}, {\"value\": -0.05399743456285877}, {\"value\": 0.9483823909192715}, {\"value\": 0.973340244224819}, {\"value\": -1.3667467673832223}, {\"value\": -1.9474088657658515}, {\"value\": 0.29515163834760766}, {\"value\": 0.42738081713721976}, {\"value\": -1.1320634249259793}, {\"value\": 0.05937092060770198}, {\"value\": 0.02265024080215617}, {\"value\": -0.3308205858139464}, {\"value\": 0.7292554382540278}, {\"value\": 0.7422970579700056}, {\"value\": 0.8506944717419468}, {\"value\": -0.8345301819256092}, {\"value\": 0.5151665004831565}, {\"value\": 0.7047915075863518}, {\"value\": -0.6506494543268511}, {\"value\": -0.5886988044496119}, {\"value\": -0.28834155386951354}, {\"value\": -0.11046682144177335}, {\"value\": 0.1219984737395238}, {\"value\": 0.7981580159087787}, {\"value\": -0.11187263555743888}, {\"value\": 0.09339132078214296}, {\"value\": 1.830542425760648}, {\"value\": 0.23427525366798038}, {\"value\": 0.9425625297891832}, {\"value\": 1.679029813382234}, {\"value\": 0.44644945818453824}, {\"value\": 2.4309555709939206}, {\"value\": -1.7295623092386467}, {\"value\": -0.6590881222115037}, {\"value\": -0.7916493405368649}, {\"value\": 0.3248718052347434}, {\"value\": -1.860259774482085}, {\"value\": -0.7144255555363089}, {\"value\": 1.5625731280893274}, {\"value\": 0.6384809401931641}, {\"value\": -1.8365457833561785}, {\"value\": -2.2525708934571043}, {\"value\": -0.5238603336351414}, {\"value\": 2.533278812111043}, {\"value\": -1.174166623510727}, {\"value\": -1.3137116099513175}, {\"value\": 0.09348257576785081}, {\"value\": -1.024092681613573}, {\"value\": 1.1285189177410757}, {\"value\": -0.2755342792838492}, {\"value\": -0.6105447810366766}, {\"value\": 0.06955726193175119}, {\"value\": 1.6056579388573908}, {\"value\": -0.08565729455613774}, {\"value\": 0.10237335011618956}, {\"value\": -0.017315978665607332}, {\"value\": 0.7864292931772117}, {\"value\": 1.2514095562880796}, {\"value\": 1.8741189861783651}, {\"value\": 0.2726205034297839}, {\"value\": -0.5690252153358643}, {\"value\": -0.15718851700741002}, {\"value\": 0.1063258636242539}, {\"value\": -0.44581824365004297}, {\"value\": 1.3742474312628936}, {\"value\": -0.2756819558351405}, {\"value\": 1.089702757543052}, {\"value\": 0.16088469071205783}, {\"value\": -0.25838639529517077}, {\"value\": -0.4946438589009543}, {\"value\": 1.1390118748318525}, {\"value\": -1.7816149033585154}, {\"value\": 0.7576828749570459}, {\"value\": 1.2520985669063927}, {\"value\": -0.7067444474872017}, {\"value\": -0.7036006970172238}, {\"value\": 0.26676765462917057}, {\"value\": 0.14786793677411358}, {\"value\": 1.3851005085701287}, {\"value\": 2.0420298805665134}, {\"value\": -1.53652586056717}, {\"value\": -0.4253214786177511}, {\"value\": -1.2097646577963748}, {\"value\": -0.9975658849488998}, {\"value\": -0.49805899881577054}, {\"value\": 0.4299033508954919}, {\"value\": 0.5050896945862}, {\"value\": 0.028260039108727063}, {\"value\": 0.32598903464523354}, {\"value\": -1.4405381696099988}, {\"value\": -0.5647951352427932}, {\"value\": -0.3780780552859521}, {\"value\": -0.3518678313031135}, {\"value\": -0.5373951553814486}, {\"value\": 0.941305844036226}, {\"value\": -0.7205491238817856}, {\"value\": 3.2859722990005196}, {\"value\": -1.4928261950922017}, {\"value\": 0.7585599631150556}, {\"value\": -0.1637462008723255}, {\"value\": 0.070616322301442}, {\"value\": 1.4705068420533198}, {\"value\": 0.6415898468020699}, {\"value\": -0.48360131908395576}, {\"value\": -0.8623632999426621}, {\"value\": -0.3696316310079534}, {\"value\": 0.39585253727640834}, {\"value\": 0.6552068139813619}, {\"value\": -0.05054768055267291}, {\"value\": 0.7955472873099246}, {\"value\": 0.43840143035189727}, {\"value\": 0.1855051638690527}, {\"value\": -0.679644199741739}, {\"value\": 0.16635482996794684}, {\"value\": 1.4031335038777384}, {\"value\": 0.7310465223219939}, {\"value\": -0.16533294741549406}, {\"value\": 0.33686507106663266}, {\"value\": -0.8636931952489686}, {\"value\": 0.5799262733439945}, {\"value\": -0.751903276081415}, {\"value\": -0.9207923672528626}, {\"value\": 1.2638049913862972}, {\"value\": 0.8176617308779266}, {\"value\": 2.6282566008062114}, {\"value\": 0.4845397983549338}, {\"value\": 0.689386502202875}, {\"value\": 0.3775051464083332}, {\"value\": 0.20517894147084226}, {\"value\": 2.674206070206671}, {\"value\": -1.3282618461875344}, {\"value\": -1.1573376486884388}, {\"value\": -0.3136248053723622}, {\"value\": 0.20970708222928075}, {\"value\": 0.2880651493310781}, {\"value\": -0.5395540222661507}, {\"value\": -0.9307008683226943}, {\"value\": 0.20432283528026943}, {\"value\": -0.8592188993729848}, {\"value\": 1.4157149851015858}, {\"value\": -1.037282969011863}, {\"value\": 0.18156810527407927}, {\"value\": -0.11064773597396699}, {\"value\": -1.4558461312424522}, {\"value\": -0.13530822872322523}, {\"value\": 0.4273320254972498}, {\"value\": 1.186777756526024}, {\"value\": -1.152071759075842}, {\"value\": 2.6240138613448374}, {\"value\": 0.15056682477015698}, {\"value\": 0.8555693587208741}, {\"value\": -1.8980521467815656}, {\"value\": 0.8321024527439458}, {\"value\": -2.2584839891130497}, {\"value\": 0.47266567997054354}, {\"value\": -1.535228715844199}, {\"value\": -2.535159019554169}, {\"value\": 0.27217590563072996}, {\"value\": 0.04038919586229305}, {\"value\": 1.0227254332220024}, {\"value\": -0.2710813345901181}, {\"value\": 1.4953832528639195}, {\"value\": -0.07378182058331566}, {\"value\": -0.6603817996467867}, {\"value\": 0.9043284040308163}, {\"value\": -0.9078305385001666}, {\"value\": -1.623884926536813}, {\"value\": -0.5189255592315631}, {\"value\": -0.21104660207986878}, {\"value\": 0.19096770566276486}, {\"value\": -0.5690994481014335}, {\"value\": -1.8778462207891715}, {\"value\": -0.3237833285519925}, {\"value\": -0.06510226529035751}, {\"value\": -0.9742183409231362}, {\"value\": -0.4310434197272873}, {\"value\": 0.27562524841151814}, {\"value\": 1.1371246603138168}, {\"value\": -0.09420653070775463}, {\"value\": -0.7163030734680983}, {\"value\": 0.6587767305206385}, {\"value\": 0.7174291867796578}, {\"value\": 0.30379974953575084}, {\"value\": -0.26797948586786025}, {\"value\": -0.0678258039312842}, {\"value\": 1.1869207200570135}, {\"value\": 0.21163091501064366}, {\"value\": -0.6938677122224621}, {\"value\": 0.03874747476472564}, {\"value\": -0.3103040651121826}, {\"value\": 1.1949919754024776}, {\"value\": -0.5420002406910596}, {\"value\": 2.917193149559914}, {\"value\": -0.7484332877132677}, {\"value\": -0.6801206186529499}, {\"value\": -0.6331017450428172}, {\"value\": 0.16237019425171026}, {\"value\": -0.5182383825228339}, {\"value\": -1.733482248769253}, {\"value\": 0.4238259139509573}, {\"value\": 0.02319116108348384}, {\"value\": 0.32030079913689646}, {\"value\": 0.9291739230240982}, {\"value\": -0.247491296284438}, {\"value\": 0.31510474153694257}, {\"value\": -0.186152107229532}, {\"value\": 0.21870811404633425}, {\"value\": 1.043535470020408}, {\"value\": 0.46971445679138174}, {\"value\": -0.025272684064452496}, {\"value\": 0.8451350765186415}, {\"value\": 0.7364525074712561}, {\"value\": 0.48291656219283796}, {\"value\": -0.8970158541097798}, {\"value\": -0.5011188739782079}, {\"value\": -1.1637678102376428}, {\"value\": 1.509528438634534}, {\"value\": 0.8418038161852809}, {\"value\": -0.8731978571079259}, {\"value\": 0.6433306434959678}, {\"value\": 0.41022495789921565}, {\"value\": -2.0030277785630823}, {\"value\": -1.6837411645773295}, {\"value\": -2.0709178667814534}, {\"value\": -0.37855308472787086}, {\"value\": -1.485220187580822}, {\"value\": -0.3388039092872563}, {\"value\": -1.2280836894234144}, {\"value\": -0.5099428834764956}, {\"value\": -1.0056280691080046}, {\"value\": -1.091652039725823}, {\"value\": 0.5646944348813953}, {\"value\": 1.2164694378078105}, {\"value\": -2.5424179916940814}, {\"value\": -0.5125095304740785}, {\"value\": -1.2133015332720385}, {\"value\": 0.17884503260420867}, {\"value\": -2.4838197106670123}, {\"value\": 0.8596790209523572}, {\"value\": -1.076841389573783}, {\"value\": 0.6301405492035002}, {\"value\": 0.38226366409875107}, {\"value\": 0.3188205105949357}, {\"value\": -1.5984853821869476}, {\"value\": -0.7277162116238184}, {\"value\": -1.4815852635349624}, {\"value\": -0.18649307159377732}, {\"value\": -0.880378488353773}, {\"value\": -1.0813897592192792}, {\"value\": 1.127880870929919}, {\"value\": -0.07425032837558763}, {\"value\": -0.258262744607094}, {\"value\": -1.132160305268288}, {\"value\": -1.0884248806581525}, {\"value\": 0.2980796315016653}, {\"value\": -0.6269578849923744}, {\"value\": -1.7774465295200241}, {\"value\": 0.13988229052391266}, {\"value\": 0.14106089150467732}, {\"value\": -0.9214174115293574}, {\"value\": -1.6946997575243332}, {\"value\": 0.49910104222809143}, {\"value\": 0.017097830208553034}, {\"value\": -0.9782441122306498}, {\"value\": 1.6710071846284635}, {\"value\": -0.2806480703524774}, {\"value\": -1.859455461398613}, {\"value\": -0.5042899093046441}, {\"value\": 2.4689612613137113}, {\"value\": -2.2495811617572916}, {\"value\": -1.1104980705852665}, {\"value\": -1.4617768258557124}, {\"value\": 0.06996354643106163}, {\"value\": 0.5371601546770833}, {\"value\": 0.7884005312152664}, {\"value\": 1.302507688161594}, {\"value\": 0.6282079312722282}, {\"value\": -0.24654213734916475}, {\"value\": -0.2126444123658046}, {\"value\": -0.4938107831027056}, {\"value\": 1.1781120519806987}, {\"value\": 0.9122521981664721}, {\"value\": -1.130151700370166}, {\"value\": -1.261567599605375}, {\"value\": -0.26663477204309016}, {\"value\": -1.148036758832816}, {\"value\": -0.767090618100979}, {\"value\": 0.1179383737376238}, {\"value\": 0.4878845203031098}, {\"value\": 0.2130826619337646}, {\"value\": 0.8203586928653768}, {\"value\": -0.05435685236708508}, {\"value\": -0.9549096759029597}, {\"value\": -0.6104311482283971}, {\"value\": -0.7231125032516531}, {\"value\": -2.0469387548532207}, {\"value\": -0.4795363016604071}, {\"value\": 1.8000924299679}, {\"value\": 0.205878836086064}, {\"value\": -1.7542978687741047}, {\"value\": 1.1053626924256434}, {\"value\": -0.6987489746776179}, {\"value\": 2.512677164151498}, {\"value\": -0.06836733222683855}, {\"value\": -1.3622330255056316}, {\"value\": -0.9853226676854939}, {\"value\": -1.2921663863872563}, {\"value\": 0.20698502943462183}, {\"value\": -1.8700111590090418}, {\"value\": 1.397713114989726}, {\"value\": 0.40403031701975994}, {\"value\": -0.5217250328187103}, {\"value\": -0.17896352176322142}, {\"value\": -0.23023603143941795}, {\"value\": -1.1641706927543622}, {\"value\": -2.1871415706998882}, {\"value\": 0.6180955219360876}, {\"value\": -0.28768957873354906}, {\"value\": -0.26509684495827734}, {\"value\": -1.0264988785181062}, {\"value\": -0.44055678098656975}, {\"value\": -0.2833627064541178}, {\"value\": 0.15307391680020824}, {\"value\": -0.023275013539791462}, {\"value\": -1.702999460978473}, {\"value\": 0.37569967327024084}, {\"value\": 0.7761130151433887}, {\"value\": 1.4488633677723668}, {\"value\": -0.4814276577355051}, {\"value\": 0.9954032548377659}, {\"value\": 1.2477724957491578}, {\"value\": 0.03070302138735071}, {\"value\": 0.5755684954481971}, {\"value\": -1.6156731475219344}, {\"value\": 1.1250125593100389}, {\"value\": -0.4187453253251842}, {\"value\": -0.6570897935228494}, {\"value\": 0.5583448945503131}, {\"value\": -0.10431670940041275}, {\"value\": -0.12194984424385046}, {\"value\": -0.8047358186636729}, {\"value\": -0.3277231036296454}, {\"value\": 0.8043611098607224}, {\"value\": -1.5501572122445872}, {\"value\": 0.6426172655682139}, {\"value\": -0.9141787652923951}, {\"value\": 1.412963842156932}, {\"value\": 0.7991885365215173}, {\"value\": 0.8798250932813894}, {\"value\": 0.3839583226696797}, {\"value\": -0.7398611096417205}, {\"value\": -0.9278398204910179}, {\"value\": 0.15738526262515018}, {\"value\": 0.4277807963541969}, {\"value\": 0.2712910291490586}, {\"value\": 0.5721323305509908}, {\"value\": -0.6723982152770264}, {\"value\": 0.8654790393085683}, {\"value\": -0.48975672678470805}, {\"value\": 0.7175957070613347}, {\"value\": -0.5152602327238728}, {\"value\": 0.5215807210694315}, {\"value\": 1.0358905066884516}, {\"value\": -0.7596879880537836}, {\"value\": 0.8385550434394436}, {\"value\": -0.16486889382985076}, {\"value\": 0.816397799539044}, {\"value\": -0.8666541375905891}, {\"value\": 0.17964767417617053}, {\"value\": 0.2417092623828831}, {\"value\": 0.5659752518965508}, {\"value\": 0.9328326439831088}, {\"value\": 1.3881716882555957}, {\"value\": 0.9351423683572042}, {\"value\": -1.176264345516955}, {\"value\": -0.9624708231868793}, {\"value\": 0.12398667660412054}, {\"value\": -1.0573993379952802}, {\"value\": 0.08256101496974874}, {\"value\": -0.6294581135422416}, {\"value\": 1.1074024197861336}, {\"value\": 0.7898312551221869}, {\"value\": -0.6251530545005263}, {\"value\": -0.7295945300486182}, {\"value\": 0.4501274071364534}, {\"value\": -1.0152393411698213}, {\"value\": 0.6998287016479077}, {\"value\": 0.35955560148863236}, {\"value\": 0.04577486953518571}, {\"value\": -1.2859131072507315}, {\"value\": -1.454784994610057}, {\"value\": -0.4574000494339981}, {\"value\": 0.6163008092077128}, {\"value\": -0.18673838461479303}, {\"value\": 0.3421626780719135}, {\"value\": -1.2063097570977057}, {\"value\": 0.2179018656963813}, {\"value\": 0.9475626506006964}, {\"value\": -0.21841375429524942}, {\"value\": 0.6278197452932849}, {\"value\": -0.9390077189129951}, {\"value\": 2.635300027142917}, {\"value\": 0.5632323608831212}, {\"value\": 0.03286953526290272}, {\"value\": 0.4211716204720785}, {\"value\": 0.8542744511504592}, {\"value\": -0.3587468538626758}, {\"value\": 0.3180163720290585}, {\"value\": 0.43904884890019286}, {\"value\": -0.8867800894895446}, {\"value\": -0.2109578278822343}, {\"value\": -0.1589235721192768}, {\"value\": 0.038187645835151}, {\"value\": 0.37946940017036074}, {\"value\": 1.3241819212867536}, {\"value\": -0.8192653837137863}, {\"value\": 1.1463722485497272}, {\"value\": -0.4294582100816717}, {\"value\": -0.6603320713524039}, {\"value\": 0.6739111621434362}, {\"value\": -0.34439985258012007}, {\"value\": -0.28418237284884196}, {\"value\": -0.15197277605261603}, {\"value\": -0.29504466443629984}, {\"value\": -0.052431403080936696}, {\"value\": 0.014270065814373666}, {\"value\": -0.2567703409048509}, {\"value\": 1.4913907571575535}, {\"value\": -0.3878712705950658}, {\"value\": 0.7398141387493146}, {\"value\": 0.09481047071398506}, {\"value\": -1.1634197616946316}, {\"value\": -1.8870437016808101}, {\"value\": -1.3705903564051014}, {\"value\": 0.4657550639113074}, {\"value\": -0.7649384680019257}, {\"value\": 0.06653312780467878}, {\"value\": 0.03541442398607965}, {\"value\": 0.742950734654999}, {\"value\": -0.6945317792713863}, {\"value\": -1.2372811476510217}, {\"value\": -0.34622132510251674}, {\"value\": -1.206490917228305}, {\"value\": -0.4393736790731636}, {\"value\": -0.3398197365823958}, {\"value\": 0.09489063696477161}, {\"value\": -0.12948372874299346}, {\"value\": -0.22882795578615703}, {\"value\": -0.28045129452534656}, {\"value\": -0.6327409381909151}, {\"value\": 1.0953489325312442}, {\"value\": 0.22765882770211326}, {\"value\": 0.9205646094641197}, {\"value\": 0.15586555757374285}, {\"value\": 1.2600071228354712}, {\"value\": -0.045921916279698}, {\"value\": -0.2104847444614215}, {\"value\": -0.7719562355055212}, {\"value\": -1.7312584210936597}, {\"value\": 0.24723778255995538}, {\"value\": 0.5807357980024687}, {\"value\": 0.09415079051254795}, {\"value\": -0.15904653382396888}, {\"value\": 0.9337261529578595}, {\"value\": -0.4201218730994765}, {\"value\": -0.3866572573088383}, {\"value\": 0.13129913939712218}, {\"value\": 1.2195359910976231}, {\"value\": 0.5941468839932359}, {\"value\": -1.7976060197645916}, {\"value\": -0.051369426772103634}, {\"value\": -0.10289880926510442}, {\"value\": 0.6334571892912596}, {\"value\": -1.9111246146530103}, {\"value\": 0.15439123662086984}, {\"value\": -0.08321378820320824}, {\"value\": -0.7612345321850474}, {\"value\": 1.134759071469142}, {\"value\": 0.387802252423988}, {\"value\": -1.0209613173386907}, {\"value\": -0.6861823027093414}, {\"value\": -1.2698045203676598}, {\"value\": -0.25290206379772606}, {\"value\": -1.003896459733733}, {\"value\": -1.4080594019425916}, {\"value\": -1.2267160071539516}, {\"value\": 0.9132794096137125}, {\"value\": 0.036897954632165636}, {\"value\": 2.428872053084167}, {\"value\": -0.43157502879957355}, {\"value\": -0.9378830100465756}, {\"value\": -0.632959324377465}, {\"value\": -0.11773489059916542}, {\"value\": 0.807962964880006}, {\"value\": -0.14137115865485683}, {\"value\": -0.9464476371681052}, {\"value\": 0.9069916587427146}, {\"value\": 0.38942587582380556}, {\"value\": -0.05475839041954973}, {\"value\": 1.6153488934609965}, {\"value\": 0.6134131846684412}, {\"value\": 0.4061763656739521}, {\"value\": -0.2558701069276286}, {\"value\": -0.8984942873803089}, {\"value\": -0.5673907212148607}, {\"value\": -0.08420395918481964}, {\"value\": 0.3993796957431279}, {\"value\": 0.33161103849983836}, {\"value\": 0.006676560839560509}, {\"value\": 0.729492336445188}, {\"value\": 1.2930069864239546}, {\"value\": 0.9885339677497418}, {\"value\": 1.4641270832808821}, {\"value\": 0.11892300710275694}, {\"value\": 0.35092214006700123}, {\"value\": 0.2966355776184408}, {\"value\": 1.1583663458887878}, {\"value\": 0.61212326710083}, {\"value\": 1.6788654275007087}, {\"value\": 0.12549440451416657}, {\"value\": -0.392625991110768}, {\"value\": 0.8636754821257006}, {\"value\": 2.471816741467148}, {\"value\": 0.9043648198496852}, {\"value\": -0.0012374269610911303}, {\"value\": -0.3298424022848336}, {\"value\": -0.7885255903366363}, {\"value\": 1.692665388850726}, {\"value\": 1.6337802625464786}, {\"value\": -0.03907125374427736}, {\"value\": -1.8791599514970003}, {\"value\": 0.20412170992211334}, {\"value\": -0.33776092330690866}, {\"value\": 0.6218080944553839}, {\"value\": 0.03159695863852286}, {\"value\": -0.20877795586569933}, {\"value\": -0.20077520922414094}, {\"value\": -0.38064844033946627}, {\"value\": -0.7435332309925231}, {\"value\": -0.9005522347198791}, {\"value\": -0.7010360328513487}, {\"value\": -1.5614981864593305}, {\"value\": -1.0374107972280249}, {\"value\": -0.5115952380882557}, {\"value\": -1.4314405974065265}, {\"value\": 1.578024442800835}, {\"value\": -0.6260251644814199}, {\"value\": -1.1481933579539798}, {\"value\": -2.3392491956691384}, {\"value\": 0.4138353520670957}, {\"value\": 0.7812252389237551}, {\"value\": -1.1003967889057558}, {\"value\": 0.32155852707748317}, {\"value\": 0.10583497755194014}, {\"value\": 0.2879780570670557}, {\"value\": -1.532726611116907}, {\"value\": 0.06335916306946832}, {\"value\": -1.9982464550164978}, {\"value\": -0.09949660329549767}, {\"value\": -0.5220399066547029}, {\"value\": -0.07860219847623576}, {\"value\": 1.6993781700864319}, {\"value\": 0.47790608104112803}, {\"value\": 0.15478618166393396}, {\"value\": -1.5988087329811}, {\"value\": 0.6220906712472486}, {\"value\": 0.7198431800328646}, {\"value\": 1.1555853186726488}, {\"value\": -0.09694223594958824}, {\"value\": 0.9210795470438906}, {\"value\": -0.9330589949637188}, {\"value\": -0.09242155002189467}, {\"value\": 0.9227609213518889}, {\"value\": -0.5556879556741945}, {\"value\": 1.2430945548270984}, {\"value\": -0.01185834598672531}, {\"value\": 0.2930556699459754}, {\"value\": -1.1564683934445767}, {\"value\": 0.5950303534147727}, {\"value\": -0.7210619692964176}, {\"value\": 0.3650050678122438}, {\"value\": 0.140181893866068}, {\"value\": -0.10207020335925804}, {\"value\": -0.4227184872797455}, {\"value\": -1.2583213795235784}, {\"value\": -0.5347645824740471}, {\"value\": -1.477447775031844}, {\"value\": 0.627310267852294}, {\"value\": 0.7485933955425179}, {\"value\": 1.1579823949398877}, {\"value\": -1.7806067857806518}, {\"value\": -1.2463919178761844}, {\"value\": 0.34182782111293586}, {\"value\": 1.1100881696459763}, {\"value\": 0.9718632052579597}, {\"value\": 0.988711326008012}, {\"value\": 0.024223563020862326}, {\"value\": -0.7001159450790273}, {\"value\": -0.11030051489554919}, {\"value\": 0.18860664738409727}, {\"value\": -0.3305712116094119}, {\"value\": -1.1371352908640755}, {\"value\": -1.4089438299748496}, {\"value\": 0.02457308067095665}, {\"value\": 0.7998381823015537}, {\"value\": 0.46171113718691265}, {\"value\": 0.2709737474347619}, {\"value\": 0.27050336272641995}, {\"value\": 1.4628892602435823}, {\"value\": 0.3039437908937181}, {\"value\": 0.47614026918180197}, {\"value\": 0.20935378287275827}, {\"value\": -0.823301716280204}, {\"value\": 0.5236777210073615}, {\"value\": 2.1850665038904244}, {\"value\": -0.5425102920697512}, {\"value\": 1.619398098375014}, {\"value\": -0.8009839305778023}, {\"value\": 1.3971375577602425}, {\"value\": -1.4363208633033167}, {\"value\": -0.19774725909471091}, {\"value\": -0.3939268285912537}, {\"value\": 1.5373507716480395}, {\"value\": 0.6649324542294842}, {\"value\": 0.6137595991461327}, {\"value\": 1.060647883797057}, {\"value\": 0.1837343445892387}, {\"value\": -1.3880181648650955}, {\"value\": -0.7816676261097799}, {\"value\": 0.361915606192087}, {\"value\": -1.116973194800475}, {\"value\": -0.8634948380275302}, {\"value\": -1.1114332195039678}, {\"value\": 0.05671214667599851}, {\"value\": -0.8253326184809585}, {\"value\": 0.15667427641082707}, {\"value\": 1.1472163844761074}, {\"value\": -1.2579256685212001}, {\"value\": -0.5222298600166319}, {\"value\": 0.193965617048504}, {\"value\": -2.028431778159097}, {\"value\": 1.8583918100209598}, {\"value\": -1.5967993912346414}, {\"value\": -1.347100034837115}, {\"value\": -0.10220283829567871}, {\"value\": -1.2621612194531964}, {\"value\": 1.2194556090627842}, {\"value\": 0.6411023313788412}, {\"value\": -0.8270949399252675}, {\"value\": 1.3838315491306372}, {\"value\": 1.4624577109517487}, {\"value\": 1.0961851020832611}, {\"value\": 0.4656235214666301}, {\"value\": 0.4700381794607131}, {\"value\": -0.21842120200272444}, {\"value\": 1.7137327572485908}, {\"value\": -0.29984536922837735}, {\"value\": 0.3953354713495643}, {\"value\": 1.049126159332038}, {\"value\": -1.498681913093224}, {\"value\": -1.0771465630839996}, {\"value\": -0.6252862378273845}, {\"value\": 0.16555823178827486}, {\"value\": 0.7326485159369756}, {\"value\": 0.04089572978284803}, {\"value\": -0.28353985457788733}, {\"value\": 1.1050126952390225}, {\"value\": 0.10531069515066871}, {\"value\": 0.6309913591687575}, {\"value\": -1.6819110232771097}, {\"value\": -2.3028637743223164}, {\"value\": -1.062343215689292}, {\"value\": 0.2952987493804825}, {\"value\": -0.7267979527288099}, {\"value\": -1.5087903135894931}, {\"value\": 2.044374763612166}, {\"value\": 0.14708945093723375}, {\"value\": -0.5699030205273685}, {\"value\": 0.015326848247028567}, {\"value\": -1.2962409494633402}, {\"value\": -1.2456862637890582}, {\"value\": -2.1156032802814715}, {\"value\": -0.8768295430211702}, {\"value\": 1.2781805388587866}, {\"value\": 1.8511553372342873}, {\"value\": 1.1246231183095037}, {\"value\": 1.4445348757048482}, {\"value\": 0.5976940768966426}, {\"value\": -0.827104513609349}, {\"value\": -0.9778463172453412}, {\"value\": -0.4572476048556327}, {\"value\": 0.8632916147003716}, {\"value\": -0.3197159885712488}, {\"value\": 0.9157990542136799}, {\"value\": 0.5991093271430749}, {\"value\": 0.2756060503965702}, {\"value\": -0.5937018203435034}, {\"value\": -0.7218802438737457}, {\"value\": -0.02528651535828406}, {\"value\": 0.3636414548506399}, {\"value\": 0.6751840980965498}, {\"value\": 0.31982543668144375}, {\"value\": -0.9207820127690146}, {\"value\": -0.5231045272789181}, {\"value\": -0.040821750811270444}, {\"value\": 1.051853993704226}, {\"value\": 0.35267399606056743}, {\"value\": -0.5578371204624708}, {\"value\": 0.14090833695033234}, {\"value\": -0.99927004421034}, {\"value\": -0.09834803561634878}, {\"value\": -0.683165691526346}, {\"value\": -0.7519367569950084}, {\"value\": -0.2269945052627053}, {\"value\": 1.5573976851752525}, {\"value\": -0.015225012018287128}, {\"value\": -0.36766515155803825}, {\"value\": 0.5324456927749932}, {\"value\": -2.259872537827176}, {\"value\": 0.8667655198281862}, {\"value\": 1.4398442915441478}, {\"value\": 1.0948515462589168}, {\"value\": 1.3515360272592971}, {\"value\": -1.1235909296013504}, {\"value\": 1.3691332135308516}, {\"value\": 0.7547802982706168}, {\"value\": -1.770141615534438}, {\"value\": -1.1597286190313005}, {\"value\": -1.8445827924664309}, {\"value\": 2.3085511974984283}, {\"value\": 1.0136609782027206}, {\"value\": 0.906941402478138}, {\"value\": -1.926770155476991}, {\"value\": -1.1015705177678925}, {\"value\": 0.06861400161750847}, {\"value\": 0.29057125367670084}, {\"value\": 0.17130425177358893}, {\"value\": -0.17452443969251002}, {\"value\": 0.5659473098311643}, {\"value\": -0.501240853813367}, {\"value\": -0.6034648876766034}, {\"value\": 1.5823010502002333}, {\"value\": -0.25498000158427964}, {\"value\": -0.7103475702509103}, {\"value\": 1.285541015255517}, {\"value\": 1.3394523570320946}, {\"value\": -0.3987346914223603}, {\"value\": 1.0909835690318965}, {\"value\": 2.0521584654909373}, {\"value\": -1.1081916508269576}, {\"value\": -1.0531908773263738}, {\"value\": -0.027544759994674987}, {\"value\": 0.1287366669706849}, {\"value\": 0.6145173623069369}, {\"value\": 0.6042218297049556}, {\"value\": 0.2661981992471444}, {\"value\": -0.755421867259145}, {\"value\": 0.5349865570556166}, {\"value\": 0.5594279092117465}, {\"value\": 0.42071773855933525}, {\"value\": -0.792249963859784}, {\"value\": -1.7316005844474407}, {\"value\": 0.5576880249826152}, {\"value\": -0.14656500834976693}, {\"value\": 0.38126914477003976}, {\"value\": -0.8680741090206299}, {\"value\": 1.572932638500426}, {\"value\": -0.24127216465759957}, {\"value\": 2.1149642890601976}, {\"value\": 0.08951042067202955}, {\"value\": -1.731809341695953}, {\"value\": 0.9759019878523739}, {\"value\": -0.6801644808018668}, {\"value\": -1.103911710290979}, {\"value\": -1.3239414511389813}, {\"value\": 1.0885989512448304}, {\"value\": 0.8778825901252622}, {\"value\": 0.7058139622468728}, {\"value\": 1.2482325290073617}, {\"value\": 1.852143717622892}, {\"value\": 0.7260898887526173}, {\"value\": 0.3374409438362824}, {\"value\": -1.0759315490310017}, {\"value\": -0.35990006753891013}, {\"value\": -1.0849059730244581}, {\"value\": -0.6016127139322861}, {\"value\": -0.7123795905534624}, {\"value\": -0.41780868865282533}, {\"value\": 0.7818294956555766}, {\"value\": 2.005159678225734}, {\"value\": -0.09721793786740705}, {\"value\": 0.05053281731145379}, {\"value\": -0.6448114043138842}, {\"value\": -0.24509392864873458}, {\"value\": -0.23029372570995493}, {\"value\": -0.7546175251276694}, {\"value\": 0.4409659004973857}, {\"value\": 0.45790626126337985}, {\"value\": 0.5247536864833996}, {\"value\": -2.4118891797285817}, {\"value\": 1.3878945482758385}, {\"value\": 0.10648854939560409}, {\"value\": 0.6234382754198724}, {\"value\": 1.2226237122423946}, {\"value\": -0.5127630172204878}, {\"value\": -0.21748520248456968}, {\"value\": 0.1772997305030423}, {\"value\": -0.8129331788023767}, {\"value\": 1.2107308796659109}, {\"value\": 2.1166868367910423}, {\"value\": 0.384967505648521}, {\"value\": 0.8714464074891194}, {\"value\": -0.32708093093440627}, {\"value\": 0.32312544793226206}, {\"value\": 1.1382064082836238}, {\"value\": -0.9918673604611796}, {\"value\": -0.6887790016791775}, {\"value\": -0.661768635808157}, {\"value\": -0.48156771633100987}, {\"value\": 1.519005659302252}, {\"value\": 0.13881041088231733}, {\"value\": -0.03711343885830522}, {\"value\": 1.3407011678062852}, {\"value\": -0.21553286871057398}, {\"value\": 1.7030600167898406}, {\"value\": 1.5829949667285161}, {\"value\": 1.3493714746930676}, {\"value\": -0.9083120631786037}, {\"value\": -0.9213140301066762}, {\"value\": 0.5026523397323139}, {\"value\": 0.6874326573809386}, {\"value\": -1.5665006279308122}, {\"value\": -0.8560128066720188}, {\"value\": -0.2167558854118616}, {\"value\": -0.28353922510880125}, {\"value\": 1.1936656435191928}, {\"value\": 0.03561562950993257}, {\"value\": -0.7460189288077971}, {\"value\": 0.06343749849338862}, {\"value\": 0.35047669709419876}, {\"value\": 0.35725088957066087}, {\"value\": -0.9539332016983683}, {\"value\": -0.6718368275852998}, {\"value\": 0.27459427636521894}, {\"value\": -0.8833905474484471}, {\"value\": 0.05781669155470331}, {\"value\": 0.6231297234008991}, {\"value\": -0.6787654068628252}, {\"value\": -0.3184275849922199}, {\"value\": -1.5303995093178706}, {\"value\": -0.6501092071088426}, {\"value\": -0.0722566809370547}, {\"value\": -0.2101880307775361}, {\"value\": 1.5587696577596968}, {\"value\": 2.282141704194203}, {\"value\": 0.29763809927528734}, {\"value\": 0.3281696477799827}, {\"value\": -0.4039804393505574}, {\"value\": 1.4546114692159184}, {\"value\": 0.6064624067281414}, {\"value\": -1.4341730313796566}, {\"value\": -1.2169320629767972}, {\"value\": -0.3102734756649828}, {\"value\": -0.8053153108922804}, {\"value\": 0.5045761107700482}, {\"value\": 0.704028175018294}, {\"value\": 2.1489404110523274}, {\"value\": 0.9098321563188365}, {\"value\": -0.7592432892515243}, {\"value\": 0.9933426331311228}, {\"value\": -1.8341096050220638}, {\"value\": 0.05471617543170912}, {\"value\": -0.521270275465744}, {\"value\": -0.932590851000084}, {\"value\": 0.0503390770584387}, {\"value\": -0.25252735964779577}, {\"value\": 1.91617772095785}, {\"value\": 1.529431616107598}, {\"value\": -1.0666148504456867}, {\"value\": 0.569973232870622}, {\"value\": -1.339378658766195}, {\"value\": 2.676611478244938}, {\"value\": 0.14845929131147237}, {\"value\": -0.28224083951937934}, {\"value\": 0.9056830198010967}, {\"value\": 0.22831877933983954}, {\"value\": -2.2666681481405626}, {\"value\": 0.5706828842899324}, {\"value\": -0.5116217668302584}, {\"value\": 0.10644098085543365}, {\"value\": -1.5193487536557126}, {\"value\": -1.2925358086186098}, {\"value\": -0.20755212696709713}, {\"value\": 0.8360587578026578}, {\"value\": 0.43811910267949083}, {\"value\": -0.9488187419239206}, {\"value\": 2.36796319876876}, {\"value\": 0.08002712558060027}, {\"value\": -0.7572188036074239}, {\"value\": -0.01136939868388684}, {\"value\": 0.9219689943562044}, {\"value\": -0.5694232277322738}, {\"value\": 2.086158020521402}, {\"value\": 2.974805119872795}, {\"value\": -0.6326127852675666}, {\"value\": 0.3206363273228848}, {\"value\": 0.1502148449080065}, {\"value\": -0.14530946682483734}, {\"value\": 0.8088500167404576}, {\"value\": 0.6878334331276164}, {\"value\": -0.5489104379180576}, {\"value\": 0.1873726867392891}, {\"value\": -1.4718058096216942}, {\"value\": 0.4154408014352591}, {\"value\": -0.20571288014911793}, {\"value\": -0.2893333486997614}, {\"value\": -0.1634079212757957}, {\"value\": 0.24828861442264144}, {\"value\": 0.417450071606556}, {\"value\": -0.5044330836970251}, {\"value\": 0.24988607912731897}, {\"value\": 1.1393267327001904}, {\"value\": 0.24323178135166437}, {\"value\": -1.1853269886971045}, {\"value\": -1.8220493159500675}, {\"value\": -0.9307281802479608}, {\"value\": 1.2610155976960298}, {\"value\": -2.4931069064402567}, {\"value\": -0.27490966813536655}, {\"value\": -0.9626509372183101}, {\"value\": -0.43063568820191694}, {\"value\": 1.398080598568805}, {\"value\": 0.9098433438867053}, {\"value\": -2.3040171005795806}, {\"value\": -1.114337213666177}, {\"value\": -0.5516867505286203}, {\"value\": -0.2735484556290128}, {\"value\": -0.9693258674652232}, {\"value\": -2.160189144978055}, {\"value\": 0.3526038793332705}, {\"value\": -0.45741892147248875}, {\"value\": 1.9810662063222964}, {\"value\": -1.0385823768013547}, {\"value\": 1.2917013898090455}, {\"value\": 0.1879579548117674}, {\"value\": -0.3345705606356935}, {\"value\": 0.5915649466090566}, {\"value\": 0.5038762667072543}, {\"value\": 0.3988550018691931}, {\"value\": 0.029769361334390586}, {\"value\": 1.2486649542743642}, {\"value\": -0.44146182111850124}, {\"value\": 1.2636094404484004}, {\"value\": 0.77251177240422}, {\"value\": 1.477061373811956}, {\"value\": -0.5651601553523622}, {\"value\": -1.386850449648743}, {\"value\": 1.3382794565763185}, {\"value\": -1.0720071264959374}, {\"value\": 0.6583702308630566}, {\"value\": 2.491237147272559}, {\"value\": -0.40016118184997346}, {\"value\": -0.18406673231601703}, {\"value\": -1.4461642603880898}, {\"value\": 1.5074436202824453}, {\"value\": -0.5456503408674841}, {\"value\": 0.4467244187580248}, {\"value\": -0.1610594309486952}, {\"value\": 0.60462553070698}, {\"value\": -0.08830498376575391}, {\"value\": 0.1491528009453617}, {\"value\": -0.15204508797803487}, {\"value\": 1.4297298081103709}, {\"value\": 1.1032755996033703}, {\"value\": -0.30271131605959223}, {\"value\": 0.6768902935050237}, {\"value\": -1.1374594373728997}, {\"value\": 0.2887935992841858}, {\"value\": -0.9483426811201049}, {\"value\": -0.6746333534131699}, {\"value\": -0.6393916739806552}, {\"value\": -0.2720132372890359}, {\"value\": 0.8945371552599493}, {\"value\": 0.05899390406837276}, {\"value\": -1.0079288617477928}, {\"value\": -1.103641485024082}, {\"value\": -0.8671242718040313}, {\"value\": 1.5109854341665654}, {\"value\": -0.07450520831458561}, {\"value\": -1.0860006552438761}, {\"value\": -0.9865502077046779}, {\"value\": 1.6568380965965572}, {\"value\": -0.5401715670176245}, {\"value\": 0.47801560852589725}, {\"value\": -0.3902911867933769}, {\"value\": 0.8792779840231194}, {\"value\": 1.2196428844169906}, {\"value\": 1.0088619002885806}, {\"value\": -0.23481828332613747}, {\"value\": -0.7448347410083709}, {\"value\": -0.07950451284079975}, {\"value\": -0.48456459892202564}, {\"value\": -1.6329856391668973}, {\"value\": -0.31987697641738555}, {\"value\": -0.5516698798653269}, {\"value\": 1.7244165784487389}, {\"value\": 2.060601202023492}, {\"value\": -0.24331838655372287}, {\"value\": 0.19597039004578584}, {\"value\": -0.24961961878415131}, {\"value\": -0.3442546229287493}, {\"value\": 0.2287927731138286}, {\"value\": -0.6232970848171436}, {\"value\": -0.17028669144102712}, {\"value\": -0.4353345549663931}, {\"value\": 0.3806161916895789}, {\"value\": -0.18343419739526257}, {\"value\": 0.851129458928006}, {\"value\": -1.655988988006819}, {\"value\": -0.18463406025725512}, {\"value\": -1.211703302252491}, {\"value\": 1.5160990634346239}, {\"value\": 0.08225802356503673}, {\"value\": 0.6669562704907998}, {\"value\": -1.8300613726545734}, {\"value\": -0.19887736206347412}, {\"value\": -0.4526887666811376}, {\"value\": -0.6919175035850164}, {\"value\": 1.539589551570615}, {\"value\": 0.43668803882180957}, {\"value\": -0.03743091921561024}, {\"value\": 0.4679737261998314}, {\"value\": -0.865362512440981}, {\"value\": 0.37534702969314837}, {\"value\": 1.5210178131446548}, {\"value\": 0.2538448306998469}, {\"value\": -0.42930535534711944}, {\"value\": -0.33529235423248055}, {\"value\": 0.08398783465796637}, {\"value\": 1.447678300244005}, {\"value\": 0.5411326484965049}, {\"value\": -0.14845655622134724}, {\"value\": 0.7837507700385387}, {\"value\": -1.1866428600453536}, {\"value\": 0.33041102490934093}, {\"value\": -0.35807842495815595}, {\"value\": 1.0373160138684032}, {\"value\": 2.2769449584511947}, {\"value\": 1.1780800227541919}, {\"value\": -0.24064997078606287}, {\"value\": 0.5541735250499712}, {\"value\": 1.266063218519576}, {\"value\": 1.101227294948142}, {\"value\": 1.303159019014591}, {\"value\": 1.3423480029841464}, {\"value\": 0.6047523717754444}, {\"value\": 0.8115691187591141}, {\"value\": -1.370697347136452}, {\"value\": 1.0226462828906462}, {\"value\": -0.14506673737056033}, {\"value\": 0.680822467589089}, {\"value\": -0.1287268080337794}, {\"value\": 1.8665534786844251}, {\"value\": 1.536789044915409}, {\"value\": -0.5471764209091227}, {\"value\": 0.19700222863540207}, {\"value\": 0.32283957080939085}, {\"value\": 1.0880268597698113}, {\"value\": -0.930396556629278}, {\"value\": -0.0058910309649104755}, {\"value\": 0.34472338779804323}, {\"value\": 0.37628568713960264}, {\"value\": -0.32571592066003013}, {\"value\": -0.6184281736825369}, {\"value\": -1.3732234485193213}, {\"value\": 0.3959386652742176}, {\"value\": 0.3187147185769787}, {\"value\": -0.8357258011987074}, {\"value\": -1.6945025995142806}, {\"value\": 0.15270774575726806}, {\"value\": 0.5720296650272022}, {\"value\": 0.0020933618350954647}, {\"value\": 1.2687823290160454}, {\"value\": 1.0242338376194662}, {\"value\": -0.2706505464213683}, {\"value\": -0.2149483136325539}, {\"value\": 0.14716129682947077}, {\"value\": -1.316982258282546}, {\"value\": 1.6592784072622433}, {\"value\": -2.146255360250473}, {\"value\": -0.5632894503408229}, {\"value\": 1.579074721462775}, {\"value\": 1.3871019071246362}, {\"value\": 0.2209859795874933}, {\"value\": -1.7598199276886606}, {\"value\": -1.2761540123356112}, {\"value\": -0.5313370675072898}, {\"value\": 0.4311979481208096}, {\"value\": -1.0237111714382936}, {\"value\": 0.7695380769761109}, {\"value\": 1.545184919085362}, {\"value\": -0.6031787249112714}, {\"value\": 0.5484986879619838}, {\"value\": 0.8434419642498043}, {\"value\": -1.897295547012907}, {\"value\": 1.324705897715799}, {\"value\": -1.022365264878498}, {\"value\": -1.1125022401326663}, {\"value\": -1.538550948089779}, {\"value\": -0.06597922333439243}, {\"value\": -1.5806541255274809}, {\"value\": 0.5231050785612594}, {\"value\": -0.43311891463924}, {\"value\": -0.3570549347314656}, {\"value\": -0.2238850289970177}, {\"value\": -1.1216391973042272}, {\"value\": 1.3611530210596674}, {\"value\": -0.6733267017050546}, {\"value\": -2.244074775593143}, {\"value\": -0.6385028467563847}, {\"value\": -0.8418560895716468}, {\"value\": 1.960605582363272}, {\"value\": 1.1550302888728525}, {\"value\": 2.0890117008086913}, {\"value\": 0.08849702668380222}, {\"value\": -0.0065563502006720795}, {\"value\": 0.7696557941347482}, {\"value\": 1.9577517919539493}, {\"value\": -0.8154542891945779}, {\"value\": -0.44735232381585005}, {\"value\": 1.3484260046869494}, {\"value\": 0.17885415714003425}, {\"value\": 0.8418875121177343}, {\"value\": -0.7356585331666619}, {\"value\": 0.8922144164086778}, {\"value\": -0.9598480692930883}, {\"value\": -0.6822201685612549}, {\"value\": -1.4159826828639404}, {\"value\": 0.3562848268066091}, {\"value\": -0.4128777918710827}, {\"value\": -0.1857215494198849}, {\"value\": 1.6584258807747057}, {\"value\": -0.155954304523548}, {\"value\": 1.2900334704079885}, {\"value\": -2.0074763710198558}, {\"value\": -0.6776336077164341}, {\"value\": 0.4376264309212599}, {\"value\": -0.21810017722967773}, {\"value\": -1.4983472998502887}, {\"value\": -0.4283250991592671}, {\"value\": 0.8308134982920397}, {\"value\": 2.4427566961934}, {\"value\": 0.828127453661501}, {\"value\": -0.5782720355286077}, {\"value\": -0.48206608710828464}, {\"value\": 0.533365556384081}, {\"value\": 0.6658279617718497}, {\"value\": -1.735085759989027}, {\"value\": -1.1249982926415723}, {\"value\": -1.0986922754178872}, {\"value\": -0.07437007981675281}, {\"value\": 0.13776435961165043}, {\"value\": -1.002865641653231}, {\"value\": -0.5258818741456255}, {\"value\": -0.18890361066781045}, {\"value\": -0.5786310819912132}, {\"value\": 0.14750982756040734}, {\"value\": 0.4687703099408197}, {\"value\": -0.7452494556987078}, {\"value\": 1.345030360133718}, {\"value\": 0.498743735605685}, {\"value\": 1.191015194850553}, {\"value\": -1.7016542222461761}, {\"value\": -0.18437652976975094}, {\"value\": -0.5374961224641436}, {\"value\": -1.109285545117789}, {\"value\": -0.06406559071255433}, {\"value\": 2.4039518625188214}, {\"value\": 0.2740277083001686}, {\"value\": 0.5422453106813023}, {\"value\": -0.8328648065492041}, {\"value\": 0.11101576923873628}, {\"value\": -1.1250338681914622}, {\"value\": 0.40003614840870344}, {\"value\": -0.8852838058506042}, {\"value\": 0.1596133596680514}, {\"value\": -1.3553978936921662}, {\"value\": 0.043723850158096336}, {\"value\": 0.10057969976588585}, {\"value\": -1.8402907844735616}, {\"value\": -0.1620546072725805}, {\"value\": -1.5587155617118378}, {\"value\": -1.2014606391324276}, {\"value\": 0.5774571829992498}, {\"value\": -0.2719204065431}, {\"value\": -1.790361039745379}, {\"value\": 0.1845766349896764}, {\"value\": 0.5411016794926303}, {\"value\": 0.7167570723557147}, {\"value\": -0.10714301616889117}, {\"value\": -0.676217114148162}, {\"value\": -1.3284344918241136}, {\"value\": -0.3787902738626277}, {\"value\": -0.4813411846799122}, {\"value\": 0.18554912810628166}, {\"value\": 0.32025486599069763}, {\"value\": 1.1467077178834988}, {\"value\": -1.1314606840721546}, {\"value\": -0.2218948797069846}, {\"value\": -0.05277416625130402}, {\"value\": -1.7448473757313123}, {\"value\": 0.7442017691414623}, {\"value\": -1.7507495271451703}, {\"value\": 0.7883238102415411}, {\"value\": -0.49705613707670254}, {\"value\": -1.6123800143758766}, {\"value\": -1.3410581950165934}, {\"value\": -1.2987908667574486}, {\"value\": -0.5077146428489102}, {\"value\": 0.5427401837584872}, {\"value\": -0.27226769630150993}, {\"value\": -0.02089299799394148}, {\"value\": -0.43395048041608214}, {\"value\": -1.1476996891744506}, {\"value\": 0.99477272652438}, {\"value\": -0.4621469908841054}, {\"value\": -0.25668414848885596}, {\"value\": 0.6016579030045467}, {\"value\": -0.3855570760422548}, {\"value\": 0.5514649258200672}, {\"value\": -0.1914509002755825}, {\"value\": -0.4161283967251975}, {\"value\": -0.7572149115452615}, {\"value\": -0.8945700996518815}, {\"value\": 0.4402988111866185}, {\"value\": 2.3686888063772185}, {\"value\": 1.9212965089185736}, {\"value\": -1.56702144019717}, {\"value\": -1.178610555489524}, {\"value\": 0.11861215789212405}, {\"value\": -0.6756011903291853}, {\"value\": 1.967890182008657}, {\"value\": 1.3277329182303257}, {\"value\": 0.6095028488803635}, {\"value\": 1.339817808621552}, {\"value\": 1.1818763837188226}, {\"value\": 0.9731569945257991}, {\"value\": 1.3599819127978152}, {\"value\": 0.4253914714328792}, {\"value\": 0.31099456015243926}, {\"value\": -1.3193309062208083}, {\"value\": -1.5205958623662295}, {\"value\": 1.351912663167045}, {\"value\": 0.6604821420278416}, {\"value\": -0.12022256090947922}, {\"value\": 2.1604731426386197}, {\"value\": 0.4795997123156647}, {\"value\": 1.7702040082417037}, {\"value\": 0.05012408401169564}, {\"value\": -0.647148137320768}, {\"value\": 0.9040518144929485}, {\"value\": -0.5838109467218421}, {\"value\": -0.29721171964125076}, {\"value\": 0.5520032828265893}, {\"value\": 0.4018386031570184}, {\"value\": -0.8651897592489355}, {\"value\": -0.3352322028269132}, {\"value\": 1.7248935179031193}, {\"value\": 0.06009537452574731}, {\"value\": 0.9158103884554492}, {\"value\": 0.35648516770963995}, {\"value\": 0.4144742208708349}, {\"value\": 1.9824245479077256}, {\"value\": -1.1106825204767745}, {\"value\": 1.2716068000433862}, {\"value\": -0.07383909915258044}, {\"value\": 0.09879628627229839}, {\"value\": -0.1383960001256424}, {\"value\": -0.2816229699286228}, {\"value\": -0.5198827912475268}, {\"value\": -0.34546054809615806}, {\"value\": -1.2929551347452917}, {\"value\": -1.2948740063146729}, {\"value\": 0.5503847787307917}, {\"value\": -0.004788119899528975}, {\"value\": 0.8207291927127311}, {\"value\": 0.3009439955538824}, {\"value\": 0.3675898990260413}, {\"value\": 0.7256913580905293}, {\"value\": -0.2953783663524118}, {\"value\": -0.4805317738471108}, {\"value\": -0.7952240342264436}, {\"value\": 0.06774586557822782}, {\"value\": -0.4243677530379945}, {\"value\": -0.47405351388505856}, {\"value\": 0.8874815972457253}, {\"value\": 1.6216726651941438}, {\"value\": 0.15697576504665817}, {\"value\": -1.488527754368105}, {\"value\": -0.8960820474148604}, {\"value\": 0.6208559657665427}, {\"value\": -0.40594592739637275}, {\"value\": -2.5244094960001364}, {\"value\": 2.114355138832716}, {\"value\": -0.5452051597254836}, {\"value\": -0.8004759575284452}, {\"value\": 1.2418321979223115}, {\"value\": -0.6692890383491416}, {\"value\": 0.19222395142930096}, {\"value\": 0.7438274089777688}, {\"value\": 0.24917572738912286}, {\"value\": 0.2671974917273002}, {\"value\": 0.5955705051048736}, {\"value\": 1.2688775384512614}, {\"value\": -0.6046366466804198}, {\"value\": 1.066666229462761}, {\"value\": -0.14701723047549486}, {\"value\": -0.07881393626731399}, {\"value\": 0.2372364521266061}, {\"value\": -0.4328547638022099}, {\"value\": 0.3925575479897551}, {\"value\": 0.8741470772138625}, {\"value\": 2.1580909866474585}, {\"value\": 2.194071289919777}, {\"value\": -1.4938305966586058}, {\"value\": 0.27674633811036564}, {\"value\": -0.2353000364557702}, {\"value\": 1.0068708515179308}, {\"value\": -1.0634495779143631}, {\"value\": -0.14497543018413983}, {\"value\": -0.8151660751964638}, {\"value\": 0.809179678548467}, {\"value\": 0.14379185231100616}, {\"value\": 0.4933177589115094}, {\"value\": 0.2599786149355275}, {\"value\": 0.36950871817698844}, {\"value\": 0.9258914527021641}, {\"value\": 1.4046266657577642}, {\"value\": 1.9405453211961705}, {\"value\": 0.34869821145375834}, {\"value\": 0.1478822389119042}, {\"value\": -0.5561051191761729}, {\"value\": -1.0037821375985452}, {\"value\": 0.13961468682052464}, {\"value\": -0.5419691591363764}, {\"value\": 1.6220600584628482}, {\"value\": 0.6292857792002856}, {\"value\": 0.880267931540763}, {\"value\": 0.8342613305319491}, {\"value\": 0.3882506976977916}, {\"value\": 1.2793612275501145}, {\"value\": 1.00686458051146}, {\"value\": -1.0295342884939789}, {\"value\": 0.3631939498002773}, {\"value\": -1.5072860534839223}, {\"value\": 0.7440749430884442}, {\"value\": -0.00042540721813152916}, {\"value\": -1.599224255134597}, {\"value\": -1.577865118202782}, {\"value\": -0.3240381444795708}, {\"value\": 0.8790461639290149}, {\"value\": 0.025031611820830517}, {\"value\": 0.8410794004583897}, {\"value\": -3.5427925649611463}, {\"value\": 0.28194910654239025}, {\"value\": -0.07116891942123774}, {\"value\": -0.7561284692534599}, {\"value\": -0.5461820887630296}, {\"value\": 0.23432716110913585}, {\"value\": -1.260493025599136}, {\"value\": 1.2476091875336943}, {\"value\": -1.5548015471191003}, {\"value\": 1.1519628416213605}, {\"value\": -0.10074697684782004}, {\"value\": -0.3783618572818501}, {\"value\": -0.6370754999025636}, {\"value\": 0.42501714313405786}, {\"value\": -0.1141139122950613}, {\"value\": -0.3295937410543295}, {\"value\": 1.2994095007802455}, {\"value\": 2.902914925944529}, {\"value\": 0.34274131000165103}, {\"value\": -0.3086264166544739}, {\"value\": 1.502592426177589}, {\"value\": -0.4062739999235933}, {\"value\": 0.9849685325624563}, {\"value\": -0.9125029084471196}, {\"value\": 0.1415628244724948}, {\"value\": 2.0770901497437837}, {\"value\": -0.7029533144124509}, {\"value\": 0.8266850952770534}, {\"value\": 1.1921707649393387}, {\"value\": -1.6904442860171383}, {\"value\": -0.3838705288048144}, {\"value\": -1.1729203418997556}, {\"value\": 0.8762156172825791}, {\"value\": 0.9576814986463035}, {\"value\": 0.8526906221917441}, {\"value\": -0.6611645459049516}, {\"value\": -0.6683732734380107}, {\"value\": -0.650971682008322}, {\"value\": 1.5114680048544284}, {\"value\": -1.3424532236040378}, {\"value\": 0.8917424211071847}, {\"value\": -0.8610409567086027}, {\"value\": 0.7725385322282858}, {\"value\": 1.9676776346707507}, {\"value\": 0.16522972842311334}, {\"value\": -0.27915584933082366}, {\"value\": -0.9748689524949002}, {\"value\": -0.5215115012218107}, {\"value\": -0.06459718976364055}, {\"value\": -0.02226224003047129}, {\"value\": 1.1831668925105958}, {\"value\": 1.6683026157608891}, {\"value\": -1.299553778466097}, {\"value\": 1.4664799742387702}, {\"value\": 0.3025705717892576}, {\"value\": -1.418027880409309}, {\"value\": 0.6875656129862274}, {\"value\": 1.1403158281843486}, {\"value\": 0.05127889332140936}, {\"value\": -0.39005459102078793}, {\"value\": -0.4536002611979622}, {\"value\": -0.21621892773843812}, {\"value\": -0.0868425966669497}, {\"value\": -0.049702662519505246}, {\"value\": -0.09984313692129583}, {\"value\": -0.7230469657433038}, {\"value\": -0.4298373024156082}, {\"value\": -1.3184330473435906}, {\"value\": 1.2100259671017497}, {\"value\": -0.8333682053745528}, {\"value\": 0.6572962840556559}, {\"value\": 0.2861513556172033}, {\"value\": -1.7452868979206704}, {\"value\": 0.4833732282785785}, {\"value\": -0.22438102654227773}, {\"value\": 0.26321199041595206}, {\"value\": 0.978647187945303}, {\"value\": 0.1334000479051123}, {\"value\": 0.025319520076929863}, {\"value\": -0.007356045419926703}, {\"value\": 0.3257641394556719}, {\"value\": -0.5281676696745925}, {\"value\": -0.2587432202771596}, {\"value\": 0.1445442793154456}, {\"value\": 1.1153084893098908}, {\"value\": -0.008814264013160851}, {\"value\": -2.8517806988476737}, {\"value\": -0.9790594483716621}, {\"value\": 0.8372518228093379}, {\"value\": -0.011424372252482854}, {\"value\": 1.9645897063152413}, {\"value\": 0.18920751837105318}, {\"value\": -0.422314262792324}, {\"value\": 0.596080172706256}, {\"value\": 1.3033951736862732}, {\"value\": 2.4360641207472598}, {\"value\": 0.9477988717213771}, {\"value\": -1.5344619776601618}, {\"value\": 0.10932053308806762}, {\"value\": 0.3188136778684033}, {\"value\": 0.8981680853304065}, {\"value\": 0.2669469496020968}, {\"value\": -0.13049621669148745}, {\"value\": -0.9154671616351937}, {\"value\": -0.7599271675334968}, {\"value\": 0.36480852041041634}, {\"value\": -1.2828219166551817}, {\"value\": -0.11615416708844502}, {\"value\": 2.232658770904048}, {\"value\": -1.2155334350638305}, {\"value\": 0.5558413846092516}, {\"value\": 0.8228049673288284}, {\"value\": -0.027742197882624706}, {\"value\": 0.9671042532538835}, {\"value\": -2.3589558244888713}, {\"value\": -0.41596971983463304}, {\"value\": 3.0800530045456913}, {\"value\": 0.4651412381319015}, {\"value\": 0.7451267381237545}, {\"value\": -1.8614558164655584}, {\"value\": 1.027211503745165}, {\"value\": 0.5159533191165413}, {\"value\": 0.047738830644143346}, {\"value\": -1.1132106714320646}, {\"value\": -0.13533623383097257}, {\"value\": -0.48118305823592644}, {\"value\": -0.050326512905128705}, {\"value\": -0.24305001458052722}, {\"value\": -0.9819094365509482}, {\"value\": 0.013598704829372853}, {\"value\": 0.026892718808718064}, {\"value\": 0.9317301090872687}, {\"value\": -1.3275887815211438}, {\"value\": 0.8571877864671346}, {\"value\": 0.7402627862636781}, {\"value\": 0.893277359588722}, {\"value\": 0.9285126706904483}, {\"value\": -0.3287169965228429}, {\"value\": 0.9871028479480092}, {\"value\": -0.06854496579382426}, {\"value\": -0.4506605187339016}, {\"value\": -0.711871808712222}, {\"value\": 1.396027307367041}, {\"value\": -0.8704102549735745}, {\"value\": -0.6870491411588158}, {\"value\": 0.09440961097075676}, {\"value\": 0.8872638527304159}, {\"value\": 1.0041379015188352}, {\"value\": 0.5582614818727539}, {\"value\": 0.133439479990284}, {\"value\": -0.48495824948943184}, {\"value\": -1.7060341518707636}, {\"value\": 0.8171817785635453}, {\"value\": -1.9957491697534269}, {\"value\": -0.6602577651619987}, {\"value\": -0.8971621373829103}, {\"value\": 0.14314261336897383}, {\"value\": -0.28973881960346837}, {\"value\": -0.798127231008134}, {\"value\": 2.4571876457105413}, {\"value\": 0.5383236897455904}, {\"value\": 1.2707852637367425}, {\"value\": -1.2194668156806916}, {\"value\": -0.5476409586443058}, {\"value\": -0.3389755240098012}, {\"value\": 0.1684157268217132}, {\"value\": -0.3862638975488072}, {\"value\": -0.0003699537569572056}, {\"value\": 1.25788126879153}, {\"value\": 0.9260452911987569}, {\"value\": 0.49703096873653785}, {\"value\": -0.8050770235759361}, {\"value\": 0.8814545566722879}, {\"value\": -0.41273037352488945}, {\"value\": -1.927288569790756}, {\"value\": 0.08183606329141924}, {\"value\": 1.0751299130601948}, {\"value\": -0.8868030138941946}, {\"value\": -0.9873836089927747}, {\"value\": 1.6639925298410032}, {\"value\": 0.44743439658227707}, {\"value\": 1.3077975673365827}, {\"value\": 0.7303265370086977}, {\"value\": -0.6609945480983124}, {\"value\": -0.19132212982976607}, {\"value\": 0.8644772934047884}, {\"value\": -1.9606194557374053}, {\"value\": -0.5093383198440234}, {\"value\": -1.189879760747927}, {\"value\": -2.1456552280679615}, {\"value\": -1.0452736981850967}, {\"value\": -0.054483015931231296}, {\"value\": -0.21000738018147438}, {\"value\": 1.6788857430111346}, {\"value\": -0.2714507302880992}, {\"value\": -0.10282522680900578}, {\"value\": 0.39367429137226134}, {\"value\": 0.1161759677430701}, {\"value\": -0.3082280296704094}, {\"value\": -0.3560636447583109}, {\"value\": -0.8135441205187699}, {\"value\": -0.6450035017837773}, {\"value\": 0.24477558941691224}, {\"value\": -1.7073955048465488}, {\"value\": 2.069339777624163}, {\"value\": 0.3432806189990639}, {\"value\": 0.3855970129642877}, {\"value\": -0.012098875726526714}, {\"value\": -1.2103957251956408}, {\"value\": -1.692144046703361}, {\"value\": -0.6805243309770437}, {\"value\": -2.6210165640165757}, {\"value\": -1.5272246729928054}, {\"value\": -0.09370458990968092}, {\"value\": -1.1292929743382978}, {\"value\": 0.875050782946594}, {\"value\": -2.2508832164840014}, {\"value\": 0.28316043581330935}, {\"value\": -1.310820802753195}, {\"value\": -0.4755496582324317}, {\"value\": 0.24182755898368735}, {\"value\": 0.509468989733369}, {\"value\": 0.9490718499795258}, {\"value\": 0.04010795592681373}, {\"value\": -0.2625108860326043}, {\"value\": 0.6273734574602599}, {\"value\": 1.9917867363193031}, {\"value\": -0.8781821576189893}, {\"value\": -1.4711398313128614}, {\"value\": -0.6603471816511599}, {\"value\": 0.26490339015794045}, {\"value\": -0.06104828283778415}, {\"value\": -0.05606664040335466}, {\"value\": -0.15257902603866144}, {\"value\": 2.050601846472103}, {\"value\": -0.5467651693724999}, {\"value\": -0.4741547043696605}, {\"value\": -2.093685907228846}, {\"value\": -0.7593159250466386}, {\"value\": 1.3771003405383153}, {\"value\": 0.09678782291450301}, {\"value\": -1.0991885309329856}, {\"value\": 0.9775677715483557}, {\"value\": -0.09008095801119236}, {\"value\": 1.488281032726366}, {\"value\": -0.8644256569652534}, {\"value\": -0.7803353094736606}, {\"value\": -0.888197230770371}, {\"value\": 1.6692415493535013}, {\"value\": 0.6488525152832869}, {\"value\": -1.075744567208058}, {\"value\": 1.4564774155288378}, {\"value\": -0.10513379451093069}, {\"value\": 0.9046054621280227}, {\"value\": -0.6350722258234296}, {\"value\": -0.0936791912542873}, {\"value\": -2.2440002200943905}, {\"value\": -0.9959614705350426}, {\"value\": -0.325731861966435}, {\"value\": 1.4571649351875746}, {\"value\": -0.6974978076495683}, {\"value\": -1.4546995141186732}, {\"value\": 0.4583526653301436}, {\"value\": 0.9542467890765927}, {\"value\": 1.3526741701211997}, {\"value\": -0.6995416401373828}, {\"value\": -0.4685270652488445}, {\"value\": -0.0975650010188072}, {\"value\": 0.1016886446902999}, {\"value\": 0.5374244683492804}, {\"value\": 0.46533121890244256}, {\"value\": -0.18677566904230414}, {\"value\": -1.365548104853138}, {\"value\": 0.4819630566927086}, {\"value\": -1.4869309157790658}, {\"value\": -0.8998259485663507}, {\"value\": -0.13913464100774664}, {\"value\": -0.23049120809100143}, {\"value\": 0.07714194158492461}, {\"value\": -0.7835843741177617}, {\"value\": -1.2709102107149426}, {\"value\": 0.1552873456735119}, {\"value\": 2.492705268038539}, {\"value\": 0.379172317391153}, {\"value\": -0.87745086741628}, {\"value\": 1.6913695563867936}, {\"value\": 0.806679301439219}, {\"value\": -0.5398432665220573}, {\"value\": 0.02983906837664632}, {\"value\": -0.4230263549695677}, {\"value\": -0.266717168541897}, {\"value\": -1.6204746021567735}, {\"value\": -0.043933907882494884}, {\"value\": 0.12653575736163053}, {\"value\": 0.8355476906770194}, {\"value\": -0.23047342634172144}, {\"value\": -0.4349986994304716}, {\"value\": -0.8841675652315392}, {\"value\": 0.605301907289953}, {\"value\": -1.7132269282771848}, {\"value\": -0.1832850832060037}, {\"value\": -1.2703713813197945}, {\"value\": 0.8400414307100487}, {\"value\": -0.6819429508021502}, {\"value\": -0.19212504070177996}, {\"value\": -0.8176740320643572}, {\"value\": 1.1911585475178097}, {\"value\": 0.5648958402717169}, {\"value\": -0.5411623775934896}, {\"value\": -0.2518944548428409}, {\"value\": -1.9247155112002663}, {\"value\": -0.2864586729640974}, {\"value\": -1.2370315598758006}, {\"value\": -0.1623730476765345}, {\"value\": -0.46373331385150496}, {\"value\": 1.771737357434027}, {\"value\": 2.0907731868537742}, {\"value\": 0.362850951027947}, {\"value\": -1.8320354410383057}, {\"value\": 0.5751787135732005}, {\"value\": -0.37104478695290466}, {\"value\": -0.4532168917261298}, {\"value\": 0.03587098125481125}, {\"value\": -0.5022179478726134}, {\"value\": 0.033592069135042}, {\"value\": 0.485617986339569}, {\"value\": -0.20225193028992217}, {\"value\": -0.5463034615961133}, {\"value\": 1.1394034060490374}, {\"value\": 1.2781231228057812}, {\"value\": -0.8353330623966511}, {\"value\": 0.14259935619556843}, {\"value\": -0.8402033929088152}, {\"value\": -1.2922931650488862}, {\"value\": 0.09845405041545964}, {\"value\": 0.2972783568398596}, {\"value\": -0.6763728399345682}, {\"value\": 0.148057757403964}, {\"value\": 1.2734882840673654}, {\"value\": 1.063061479633452}, {\"value\": 0.6667405916678116}, {\"value\": -0.9848251278980731}, {\"value\": 0.23910911682719338}, {\"value\": 0.23279254025846263}, {\"value\": 0.8661507704677464}, {\"value\": -0.2717641117240363}, {\"value\": 0.3990221464366555}, {\"value\": -0.3297992185266119}, {\"value\": 0.9314592308875611}, {\"value\": -2.137532218605782}, {\"value\": -0.030018900895792785}, {\"value\": -0.16924055417730458}, {\"value\": -0.06235822238341352}, {\"value\": 0.3725656385985555}, {\"value\": 1.2673587328785405}, {\"value\": -0.1829290352808399}, {\"value\": -1.0661242620721316}, {\"value\": 1.0999145738927298}, {\"value\": -0.659494356317039}, {\"value\": -1.6254046827056365}, {\"value\": 1.0649566761885485}, {\"value\": 1.7813924970462007}, {\"value\": -0.43818390350046993}, {\"value\": 0.14062378054077015}, {\"value\": 2.111537917449163}, {\"value\": -1.2880193106666147}, {\"value\": -0.17622989538491463}, {\"value\": 0.15970700184718029}, {\"value\": 1.203491027850183}, {\"value\": 0.8881680645781981}, {\"value\": 1.9349498070690183}, {\"value\": -0.6353155876018187}, {\"value\": -1.010017975989372}, {\"value\": 0.4020203585237129}, {\"value\": -0.7099159103861118}, {\"value\": 0.9546085445659206}, {\"value\": 0.6997141285125672}, {\"value\": -0.11066843607960218}, {\"value\": -1.1626648250560967}, {\"value\": -0.41362944971701476}, {\"value\": -0.279596294380501}, {\"value\": -0.08056080420975738}, {\"value\": -0.19751778411030613}, {\"value\": -0.18802476625142714}, {\"value\": -1.7171681157552159}, {\"value\": -1.0390976194674475}, {\"value\": -1.5482828276324474}, {\"value\": 0.9730388122158847}, {\"value\": -0.17665264294433652}, {\"value\": 0.5845419819274109}, {\"value\": -1.1245726331269157}, {\"value\": -0.07439496264646964}, {\"value\": 0.520006335430548}, {\"value\": 0.0795174413607225}, {\"value\": -0.19378996669495163}, {\"value\": 0.7273492214281586}, {\"value\": 0.8992270701558608}, {\"value\": -0.9921442358807838}, {\"value\": -0.8149908930289154}, {\"value\": 0.8004783161187212}, {\"value\": -0.7793732463685612}, {\"value\": -0.07518599468488892}, {\"value\": -0.05606601739214189}, {\"value\": 0.10530432562053857}, {\"value\": 1.7449557835840972}, {\"value\": 0.6005229432821091}, {\"value\": -1.4452718635835653}, {\"value\": 0.5536355596379766}, {\"value\": 0.015253220138154142}, {\"value\": 0.26483592741677187}, {\"value\": 0.6421748554652582}, {\"value\": -0.10651820918409748}, {\"value\": -0.3756503404097631}, {\"value\": 0.9984533055195277}, {\"value\": 0.01990443189724938}, {\"value\": 0.7892625836993289}, {\"value\": 0.7868293460463515}, {\"value\": 0.3282169897413826}, {\"value\": 1.4099160406907414}, {\"value\": 2.2114370251055044}, {\"value\": 0.5175115428407892}, {\"value\": 1.6481960493910477}, {\"value\": 0.8559908545221462}, {\"value\": 1.5035539978521086}, {\"value\": -1.231856656505741}, {\"value\": 0.5465710787158955}, {\"value\": 0.43712568325770207}, {\"value\": -0.4439833639702042}, {\"value\": -0.48125477404516787}, {\"value\": -1.032665149269277}, {\"value\": -0.8260520573286705}, {\"value\": 1.5970129113345881}, {\"value\": 0.7159598877922557}, {\"value\": -0.7541033989263414}, {\"value\": 1.2032143448070673}, {\"value\": -0.7333559740947526}, {\"value\": -0.8519700525113477}, {\"value\": 1.0759731237043149}, {\"value\": -0.2759628705505857}, {\"value\": 0.10051352097208055}, {\"value\": -0.07789839504341346}, {\"value\": -0.6436159976809507}, {\"value\": -0.5399030657102781}, {\"value\": -0.25314245772878097}, {\"value\": 1.1104515365506975}, {\"value\": 0.8303192235095407}, {\"value\": 0.10862981991259972}, {\"value\": 1.2721792180258575}, {\"value\": 0.48011623338101506}, {\"value\": -0.802421870686714}, {\"value\": -0.36071986168171133}, {\"value\": -0.5243598656057668}, {\"value\": -1.421750097763189}, {\"value\": -0.2942031963356094}, {\"value\": -0.09842780884630989}, {\"value\": 0.03123418316132263}, {\"value\": 1.248645035236179}, {\"value\": -0.05847304186329867}, {\"value\": 0.15929027205817065}, {\"value\": -0.14133339445236826}, {\"value\": 0.8753434148730078}, {\"value\": -0.16593543109506861}, {\"value\": 0.7500752788810279}, {\"value\": 0.4394080621894248}, {\"value\": -1.242763746566685}, {\"value\": 1.756811596902247}, {\"value\": 0.8188213461330448}, {\"value\": 0.49236387260033443}, {\"value\": -0.8917923901637129}, {\"value\": 0.14861209788943647}, {\"value\": -0.38943216563991667}, {\"value\": -1.2311598103394854}, {\"value\": -1.4430002301555351}, {\"value\": 0.5312518516973448}, {\"value\": 0.37514388164866125}, {\"value\": 0.7291908781104081}, {\"value\": 0.19289536075024327}, {\"value\": 1.881387727830607}, {\"value\": -0.47039210037605994}, {\"value\": -0.6483718435843759}, {\"value\": 0.1663456581204554}, {\"value\": 0.7407323165851161}, {\"value\": 2.4235755096200626}, {\"value\": -0.27617374339365774}, {\"value\": -0.6815934326018309}, {\"value\": 0.29622239556102337}, {\"value\": -0.7836927940776356}, {\"value\": -0.7245888174823283}, {\"value\": -0.18646184576857747}, {\"value\": -0.6006662277002095}, {\"value\": 0.39968709837055155}, {\"value\": 0.7819870169153085}, {\"value\": 0.29093621537867337}, {\"value\": -0.2916126465924258}, {\"value\": -0.6828197418016008}, {\"value\": 0.11194549914967444}, {\"value\": -0.07239029431586816}, {\"value\": 1.294295230535408}, {\"value\": -0.07468925403077431}, {\"value\": -0.9881544981734773}, {\"value\": 1.307745068998731}, {\"value\": -0.3931891663455819}, {\"value\": 0.9487741663658977}, {\"value\": 1.6637583797987099}, {\"value\": 0.942981138035614}, {\"value\": -0.720463169687677}, {\"value\": 0.385659066028673}, {\"value\": 0.17026356058648298}, {\"value\": 0.17370456446210122}, {\"value\": -0.9703886341059828}, {\"value\": 0.5467755487855805}, {\"value\": -0.08889877793093248}, {\"value\": 0.6547194154537116}, {\"value\": -1.2589800340522834}, {\"value\": 1.702082508476279}, {\"value\": -0.5629282956166314}, {\"value\": -0.5841719410044294}, {\"value\": 0.3914680195420047}, {\"value\": 0.6277007636127618}, {\"value\": -1.859833354737557}, {\"value\": -0.19567963978446556}, {\"value\": 0.599667266333348}, {\"value\": -0.12407911396330654}, {\"value\": -1.4474918831831702}, {\"value\": 0.024265723348713655}, {\"value\": 0.75170526720756}, {\"value\": 0.3605091156947127}, {\"value\": 0.3155244951386618}, {\"value\": -0.029179407918681864}, {\"value\": 0.7236801116195797}, {\"value\": 0.6336187672285662}, {\"value\": 0.7933460535357799}, {\"value\": 0.4519316377959817}, {\"value\": -1.4813099200031477}, {\"value\": -0.19538609048268707}, {\"value\": 0.537315075207976}, {\"value\": 0.9716843602457776}, {\"value\": 1.723404462297098}, {\"value\": -0.3156119269157988}, {\"value\": 0.24890193416471298}, {\"value\": 1.5912089399751586}, {\"value\": -2.1208807566261023}, {\"value\": 1.9585354163602897}, {\"value\": 0.019362699019575335}, {\"value\": 0.9607540226464851}, {\"value\": 1.3942799098783931}, {\"value\": -0.6460178770681512}, {\"value\": 0.7454825767554725}, {\"value\": 0.15807703203655}, {\"value\": -0.4325462363112261}, {\"value\": -0.0912876887591032}, {\"value\": -0.4210238727689256}, {\"value\": -0.11089954750241968}, {\"value\": 0.08215621879433405}, {\"value\": -1.3827689962405116}, {\"value\": -0.9148906197117782}, {\"value\": 1.1907092613677557}, {\"value\": -0.2967567457869889}, {\"value\": -1.7509425569032877}, {\"value\": -0.98229059648961}, {\"value\": -2.0804098514065457}, {\"value\": -0.27020752584950153}, {\"value\": 0.44398838542676083}, {\"value\": 0.6931407362032873}, {\"value\": -0.21556730788468417}, {\"value\": -0.6968649694152685}, {\"value\": 0.37589060693414655}, {\"value\": -0.7041869812581659}, {\"value\": 0.5495933853568917}, {\"value\": 0.40405775674700695}, {\"value\": 1.370898434104988}, {\"value\": -0.1426422621034018}, {\"value\": -0.5061954295915717}, {\"value\": 0.44036788080887973}, {\"value\": 0.45051263387599855}, {\"value\": 1.047296659373168}, {\"value\": 1.710240562032071}, {\"value\": 0.5125051854107278}, {\"value\": 1.07721446809341}, {\"value\": 0.6098154776187875}, {\"value\": -1.4488272360574326}, {\"value\": 0.7234295759835764}, {\"value\": 0.4832945659374271}, {\"value\": 1.9344881608290359}, {\"value\": -0.3984407422039007}, {\"value\": -0.5332911228520834}, {\"value\": 0.9549394410025207}, {\"value\": 1.2366430896425151}, {\"value\": -0.5117253261786362}, {\"value\": 0.49202615417871615}, {\"value\": -0.11109176989472604}, {\"value\": 0.4838822276508886}, {\"value\": 0.5496565930088497}, {\"value\": 0.2643846346284582}, {\"value\": 1.1962191998704277}, {\"value\": 0.33990888193631164}, {\"value\": -0.27765320355043166}, {\"value\": -0.25748379484307093}, {\"value\": -0.6468190335036602}, {\"value\": 1.1400273334283435}, {\"value\": 0.387720684670024}, {\"value\": -0.09590559532900388}, {\"value\": -0.4099461571350226}, {\"value\": -2.0745327971937906}, {\"value\": 0.5111752797288709}, {\"value\": -2.4811921105969277}, {\"value\": -0.9208867115296152}, {\"value\": 0.19986554036699417}, {\"value\": 0.2041604575017748}, {\"value\": 0.7979028285200955}, {\"value\": 0.4217341025303167}, {\"value\": -0.6362619829596843}, {\"value\": -0.8787288622142293}, {\"value\": -1.0612004005432951}, {\"value\": 0.860190805878597}, {\"value\": 0.811605252285115}, {\"value\": -2.053220410974208}, {\"value\": -0.836017225278229}, {\"value\": -1.0637172687540115}, {\"value\": -0.03940673450299658}, {\"value\": 0.6587818777860619}, {\"value\": -0.7695255139180285}, {\"value\": 2.023142974901758}, {\"value\": 0.25004777587934784}, {\"value\": -0.8427145174220824}, {\"value\": -0.21374774118155526}, {\"value\": 0.1202383533125858}, {\"value\": 1.4727192818907142}, {\"value\": -1.210350218007462}, {\"value\": -0.6911847089930946}, {\"value\": -0.4491941757783327}, {\"value\": 0.22065220616039888}, {\"value\": -1.109952813909344}, {\"value\": 0.5291232153884754}, {\"value\": -1.7814563334860898}, {\"value\": -2.0885155462536553}, {\"value\": 0.9615128025009918}, {\"value\": 1.585538804626167}, {\"value\": -0.52701388343268}, {\"value\": 1.3617553543524776}, {\"value\": 0.3933518199137531}, {\"value\": 1.1609528705155936}, {\"value\": 1.4306915420791702}, {\"value\": 1.239508453868907}, {\"value\": -0.9965719573422238}, {\"value\": -0.9874272939546154}, {\"value\": -1.2545939827767887}, {\"value\": -2.0196850332894845}, {\"value\": 0.8709171504513425}, {\"value\": 1.144271299167386}, {\"value\": -0.3606112162219209}, {\"value\": -0.9001208803555868}, {\"value\": 1.0063976649768878}, {\"value\": 0.4003887056161615}, {\"value\": -1.0462193785029918}, {\"value\": -0.09679050410598077}, {\"value\": -1.462187205053918}, {\"value\": 0.27773548660358927}, {\"value\": -0.8243956838875087}, {\"value\": 1.015955557316707}, {\"value\": 0.06559972280465916}, {\"value\": -1.5501495006452728}, {\"value\": -0.5399394317932609}, {\"value\": 2.1777210144269796}, {\"value\": 0.3144258420864662}, {\"value\": 0.6841150418805937}, {\"value\": -0.5556807293462412}, {\"value\": 1.6691337291906971}, {\"value\": -0.9451431735090501}, {\"value\": 0.19615695577761966}, {\"value\": -1.6745685398083212}, {\"value\": 0.4023458356026223}, {\"value\": -1.1603904840905297}, {\"value\": -0.711231808281413}, {\"value\": -1.237742160328628}, {\"value\": -3.3948481774221064}, {\"value\": -0.27129232384460683}, {\"value\": -0.21775491252777956}, {\"value\": 0.5444769214091086}, {\"value\": -0.5140929465358494}, {\"value\": 0.06126634267045811}, {\"value\": -1.175530604010782}, {\"value\": -0.4871981023582176}, {\"value\": -1.5270338092947189}, {\"value\": 0.58162035978236}, {\"value\": 0.859543963184442}, {\"value\": 2.2081814454003825}, {\"value\": -0.8727168795270824}, {\"value\": -0.9093673402538368}, {\"value\": -1.0416064803703786}, {\"value\": 1.8443681728405636}, {\"value\": 0.620084269963906}, {\"value\": -0.8925959778203727}, {\"value\": 0.1338783488774013}, {\"value\": -0.15903175220684337}, {\"value\": -1.955819973611869}, {\"value\": 1.05635806318147}, {\"value\": 0.7014986139235206}, {\"value\": 0.3179445480161329}, {\"value\": -0.4999624396821447}, {\"value\": -0.7318227652904934}, {\"value\": 0.438809928060698}, {\"value\": -1.2523416052106353}, {\"value\": -0.9155637195847697}, {\"value\": -0.00961914151031286}, {\"value\": 0.9322519045389102}, {\"value\": -0.3741847537485909}, {\"value\": -0.13461778277333467}, {\"value\": -0.2139796392894102}, {\"value\": -0.9639362244976055}, {\"value\": 0.4958417993341647}, {\"value\": 0.235342367499282}, {\"value\": -0.592121512570448}, {\"value\": -0.5208277904996652}, {\"value\": 0.4285751116542241}, {\"value\": -0.4551778724336462}, {\"value\": -0.06652573197952764}, {\"value\": 1.005710021874105}, {\"value\": -0.027990699799120042}, {\"value\": 0.2808088688999325}, {\"value\": -1.3913168598030494}, {\"value\": -1.0426160622923801}, {\"value\": 0.19724096061278787}, {\"value\": -3.071592070559779}, {\"value\": 1.011217577973087}, {\"value\": 0.5740691043436441}, {\"value\": -0.46322545649923696}, {\"value\": -0.31069839826543194}, {\"value\": 0.35918458502878414}, {\"value\": 0.32651946602093534}, {\"value\": -0.7760565370154149}, {\"value\": -0.9068592506753361}, {\"value\": -0.4254073958836105}, {\"value\": 0.523531839788238}, {\"value\": 1.6200610380895664}, {\"value\": 0.7149351764955251}, {\"value\": 0.03399883102098602}, {\"value\": 0.13695980075511}, {\"value\": 2.1321484855868786}, {\"value\": -1.8036603486417933}, {\"value\": -0.05066791479177613}, {\"value\": 0.7268883059679725}, {\"value\": 2.4246195026058905}, {\"value\": 1.5461500695637231}, {\"value\": 0.350273546433803}, {\"value\": 1.135681068939511}, {\"value\": 0.9951712317698981}, {\"value\": -0.7864677380251761}, {\"value\": -0.023662805766156102}, {\"value\": 0.014417736639980009}, {\"value\": -0.1587350411368056}, {\"value\": 1.3270991853981458}, {\"value\": 1.1892977892308123}, {\"value\": -1.6481793768334203}, {\"value\": 0.07506466550165175}, {\"value\": 0.9618549636815273}, {\"value\": 0.37040480975029044}, {\"value\": 0.11575199989695563}, {\"value\": 0.2648283834831996}, {\"value\": -0.802751116867496}, {\"value\": 0.34324386556575054}, {\"value\": 0.0895126706833055}, {\"value\": 0.35648151365532693}, {\"value\": -0.7392744819392061}, {\"value\": 0.7084745440608471}, {\"value\": 0.26043718156760876}, {\"value\": -0.018294413938281167}, {\"value\": -0.14381926746658472}, {\"value\": 1.417586271594416}, {\"value\": -0.22131261579056702}, {\"value\": -0.569291263580532}, {\"value\": 1.2017038900666086}, {\"value\": 1.7339759181705359}, {\"value\": 1.3762035233560554}, {\"value\": 1.012591367155816}, {\"value\": 1.5141660469228138}, {\"value\": 0.6068558340538361}, {\"value\": -0.02724050505246015}, {\"value\": 1.231202372868731}, {\"value\": -0.6856724706256433}, {\"value\": 0.26878340556264635}, {\"value\": 0.05466486830533415}, {\"value\": -0.6139411273031641}, {\"value\": -1.2410242517077081}, {\"value\": -0.4005654292513976}, {\"value\": -1.4044001250226001}, {\"value\": -0.09711532747646574}, {\"value\": 0.7178109873189679}, {\"value\": 0.32036141768754545}, {\"value\": -1.4078157000219431}, {\"value\": -0.18046445962987553}, {\"value\": 0.4756388828980532}, {\"value\": -0.9574518635995074}, {\"value\": -0.8388611359836194}, {\"value\": 0.8839523628641541}, {\"value\": 0.7631527475468852}, {\"value\": 1.5156344639785986}, {\"value\": -0.7428346945044941}, {\"value\": 0.9673801484409853}, {\"value\": -1.0810806413924463}, {\"value\": 1.3378862558413307}, {\"value\": 1.0162477914774997}, {\"value\": 0.3265672682943894}, {\"value\": -0.799002397818584}, {\"value\": 0.6260362973777138}, {\"value\": 0.6931425042306671}, {\"value\": 0.39882819982639417}, {\"value\": 1.100419443500297}, {\"value\": 1.136111314122601}, {\"value\": 1.1692653175195404}, {\"value\": 0.7189267953614331}, {\"value\": -0.44168758894103805}, {\"value\": 0.7744173970090046}, {\"value\": -0.4821429605350943}, {\"value\": 0.9972838880949867}, {\"value\": -0.2914485565250606}, {\"value\": 1.6077863596536606}, {\"value\": -0.5602097188511077}, {\"value\": 0.43554366650047915}, {\"value\": -1.0964035148716116}, {\"value\": 0.09165046163266914}, {\"value\": -0.4488245400421249}, {\"value\": -0.9966267523897118}, {\"value\": -0.6700162830346827}, {\"value\": -1.4944959282463113}, {\"value\": -0.42298771624773246}, {\"value\": -0.6150296876117307}, {\"value\": -0.5727333341054812}, {\"value\": -0.008345212169042803}, {\"value\": -2.1275070052410023}, {\"value\": 0.7486468597999034}, {\"value\": -1.6160324525592478}, {\"value\": 1.7736906833842168}, {\"value\": -0.278843200063898}, {\"value\": -0.2711603626755067}, {\"value\": 0.5646858325962179}, {\"value\": 2.159401972260811}, {\"value\": 0.01615212332965331}, {\"value\": 0.312154781372231}, {\"value\": 0.41883421562821266}, {\"value\": -2.7993646290629335}, {\"value\": -0.24515681453077132}, {\"value\": -0.290077527030733}, {\"value\": -1.9996252844408176}, {\"value\": -0.9109244249766664}, {\"value\": 0.9563256348324564}, {\"value\": 0.9199990585562616}, {\"value\": -0.06687024008467857}, {\"value\": 0.9114343747468022}, {\"value\": -0.948724648275785}, {\"value\": 1.5245903052677572}, {\"value\": 0.31862433082348657}, {\"value\": 0.6597550985033439}, {\"value\": -0.6824705734116681}, {\"value\": 1.3588026482396685}, {\"value\": -1.047140352297875}, {\"value\": -1.7614485266008548}, {\"value\": 0.7896401004118133}, {\"value\": -0.6545445597002761}, {\"value\": 0.8429428075165951}, {\"value\": -1.1959400355605252}, {\"value\": -0.46767705345140953}, {\"value\": 0.20916269167005863}, {\"value\": 0.8213007863657942}, {\"value\": -1.5195391142762043}, {\"value\": 2.3666458754998527}, {\"value\": 0.3489376777325927}, {\"value\": -0.3081298756023285}, {\"value\": -0.18043654036427087}, {\"value\": -0.3653823202897784}, {\"value\": 0.7100987466598321}, {\"value\": -0.5533807919324261}, {\"value\": -0.44071563739510017}, {\"value\": 0.6300776875758147}, {\"value\": 1.5185107041522599}, {\"value\": 0.4346371122400999}, {\"value\": 1.1930966680592894}, {\"value\": -0.23473385310980013}, {\"value\": 1.0174597786481547}, {\"value\": -0.13848524888058336}, {\"value\": 0.6866467750381698}, {\"value\": 0.3248187349192249}, {\"value\": -1.1370585236803017}, {\"value\": -0.041106532836626894}, {\"value\": 1.5011322174611401}, {\"value\": 0.8241834792730413}, {\"value\": 0.3062935522027708}, {\"value\": 0.6016026351012438}, {\"value\": -0.7345195803050901}, {\"value\": 1.173610367303582}, {\"value\": -0.041107800448722816}, {\"value\": 0.33028891143060024}, {\"value\": 1.2348548417847462}, {\"value\": -0.5332205625429987}, {\"value\": -0.027441525963412372}, {\"value\": 0.752860852448929}, {\"value\": -1.1369680143945065}, {\"value\": -0.17410046877379895}, {\"value\": 0.41087739553858676}, {\"value\": 0.39745664088126403}, {\"value\": 1.3919215173943065}, {\"value\": -1.5880916224280932}, {\"value\": -0.23114266239445816}, {\"value\": 0.0672527674475322}, {\"value\": 0.6553386926509188}, {\"value\": 1.043167506199157}, {\"value\": 0.9465423125887247}, {\"value\": -0.5699311895906983}, {\"value\": 0.63609119943045}, {\"value\": 0.541174872865483}, {\"value\": 0.8298075345186091}, {\"value\": 0.466854220371387}, {\"value\": -1.0734628868440488}, {\"value\": -0.14249256472966418}, {\"value\": 0.14133375807038243}, {\"value\": 0.6334751660291951}, {\"value\": -0.668614042549307}, {\"value\": 1.8481881582057396}, {\"value\": -0.4514390986768457}, {\"value\": -0.08789573812184588}, {\"value\": -1.0252270040551197}, {\"value\": 0.739697123169842}, {\"value\": 0.5754649868171708}, {\"value\": -0.7206644210036347}, {\"value\": -0.6033625958559518}, {\"value\": 0.5962164695670734}, {\"value\": 1.3097089508042703}, {\"value\": -0.014692831417427592}, {\"value\": 0.9768745216756463}, {\"value\": 0.7643444050830466}, {\"value\": 1.1724097556181647}, {\"value\": -0.6971543105556688}, {\"value\": -1.1870706504259685}, {\"value\": 1.4456123015717506}, {\"value\": 1.2526832398500416}, {\"value\": -1.193959032690657}, {\"value\": 0.15387336431385668}, {\"value\": 0.5318474232985954}, {\"value\": 0.571861734872873}, {\"value\": -1.6788193788204295}, {\"value\": 1.716109018280791}, {\"value\": 1.4525862300297163}, {\"value\": 1.4051326264557569}, {\"value\": 1.630253470300932}, {\"value\": -0.11635841679707945}, {\"value\": -0.13957092451351022}, {\"value\": -0.8179301783005418}, {\"value\": 1.0321524045899333}, {\"value\": -0.6732036375867547}, {\"value\": -1.1568794816628754}, {\"value\": -0.09708692302990003}, {\"value\": -0.7746392036973254}, {\"value\": 0.8977280196823338}, {\"value\": -0.0684882095452741}, {\"value\": 1.1525970943249537}, {\"value\": 0.49587306189731944}, {\"value\": 1.2130912458858603}, {\"value\": 0.2863267235108526}, {\"value\": -0.8080692643797026}, {\"value\": 1.2588609409947218}, {\"value\": 0.03717762000666612}, {\"value\": -1.1508315081426173}, {\"value\": 0.25266317422991164}, {\"value\": 0.12189782471263208}, {\"value\": -0.30407543505235407}, {\"value\": -1.0168726103707255}, {\"value\": -0.5406764322198883}, {\"value\": -0.05166941585083283}, {\"value\": 0.6978877155824802}, {\"value\": 0.12463520353857274}, {\"value\": -0.196467485098927}, {\"value\": 0.03861895104458822}, {\"value\": 1.0593801230598991}, {\"value\": 0.09329878801070245}, {\"value\": -0.7272136164480906}, {\"value\": 1.2332849830918176}, {\"value\": 0.29671696319719815}, {\"value\": 1.7637077213474686}, {\"value\": 0.2932425111927223}, {\"value\": 0.6959629057055807}, {\"value\": -0.9838179768112305}, {\"value\": 0.4676673925417568}, {\"value\": 1.2869959361324546}, {\"value\": 1.1058706290750335}, {\"value\": -0.9268215967860726}, {\"value\": 2.5954951263891863}, {\"value\": -0.7959232654664522}, {\"value\": 0.22673480862520096}, {\"value\": 0.6091111001696718}, {\"value\": 1.0281099549175938}, {\"value\": 0.7685598594319305}, {\"value\": 0.4695937678756088}, {\"value\": 0.4936777845744183}, {\"value\": 1.9297150700979648}, {\"value\": 0.5755632198011933}, {\"value\": -1.613390156841389}, {\"value\": -0.9208167704687918}, {\"value\": 0.07339661601585633}, {\"value\": -0.07722836130400297}, {\"value\": 0.4670232812415664}, {\"value\": -0.10811149355628018}, {\"value\": 0.07567329319231575}, {\"value\": 0.18736851201319102}, {\"value\": -0.292284891042758}, {\"value\": 0.6522919095827954}, {\"value\": -0.407381698862243}, {\"value\": 0.531028096872444}, {\"value\": -0.053173988615924477}, {\"value\": 1.4595499243287233}, {\"value\": -1.6666521867265436}, {\"value\": -0.8990461193999766}, {\"value\": -1.0158813810495428}, {\"value\": -1.406948976734557}, {\"value\": 0.6874120924067386}, {\"value\": -0.4003921433513914}, {\"value\": -0.6761568079346285}, {\"value\": 2.1766479741649327}, {\"value\": 0.7962334411554864}, {\"value\": -1.2060207381653045}, {\"value\": -0.6695379256049997}, {\"value\": 0.5072068382105157}, {\"value\": -0.8352927626387531}, {\"value\": -0.9311306225921085}, {\"value\": 2.6079947691332186}, {\"value\": 2.1796624994276335}, {\"value\": 0.15270530652695855}, {\"value\": 1.6724905796758962}, {\"value\": 1.697792992810792}, {\"value\": 0.19878882117326518}, {\"value\": 0.9384882462964087}, {\"value\": -0.6640603098571443}, {\"value\": 1.1660859506817483}, {\"value\": -1.4390351817063645}, {\"value\": 0.1886219001774772}, {\"value\": 1.4045752803719465}, {\"value\": -0.976424119654908}, {\"value\": 1.1958014631312632}, {\"value\": 2.079413612852157}, {\"value\": -1.1442364879902973}, {\"value\": -1.2281347466485775}, {\"value\": 0.8114509318295106}, {\"value\": -0.3616684324357761}, {\"value\": 0.2965260954967724}, {\"value\": 1.560342164045004}, {\"value\": 0.7688339721609084}, {\"value\": -0.9257853067456622}, {\"value\": 0.049737390728657}, {\"value\": -1.557499925653759}, {\"value\": -0.17413753757847114}, {\"value\": 0.12911560963445134}, {\"value\": 0.25495478163218727}, {\"value\": -0.936720295674154}, {\"value\": 0.9137300681672293}, {\"value\": 0.3432970463859185}, {\"value\": -0.4292827864666044}, {\"value\": 0.05848528288068177}, {\"value\": -0.26711905397814345}, {\"value\": 0.24381750884459377}, {\"value\": 0.8337588976646763}, {\"value\": 0.48011469056565464}, {\"value\": -0.9730570612704019}, {\"value\": -0.374227792443718}, {\"value\": -0.5319616721557762}, {\"value\": -0.6896131424567823}, {\"value\": -0.27552555035796933}, {\"value\": 2.326353311883273}, {\"value\": -0.2559215785610885}, {\"value\": 2.4941231228091865}, {\"value\": -0.08926914088681127}, {\"value\": 0.4238080413430485}, {\"value\": 3.310854111602752}, {\"value\": -0.4136166889589001}, {\"value\": 0.18580946581390564}, {\"value\": -2.451514391191801}, {\"value\": -0.7478969447691652}, {\"value\": 1.255755215319295}, {\"value\": -0.8950404579412773}, {\"value\": -0.09807822186633887}, {\"value\": -0.946083982301509}, {\"value\": 2.540930795607073}, {\"value\": 0.5818671580675544}, {\"value\": 0.38714221342971616}, {\"value\": 0.46164767503336895}, {\"value\": -0.4174441845198614}, {\"value\": 0.5514648870990823}, {\"value\": 0.703175310905804}, {\"value\": -0.27276397216841214}, {\"value\": 0.5947261439240268}, {\"value\": 1.2963683289369012}, {\"value\": -0.16373201789641573}, {\"value\": 0.07669090370181623}, {\"value\": 0.9367954667929304}, {\"value\": 2.275670944819355}, {\"value\": -1.614234698768038}, {\"value\": -1.7346689515476006}, {\"value\": 0.3255831745315176}, {\"value\": 0.14738600824513723}, {\"value\": -0.2802671188496263}, {\"value\": -0.060023752400590547}, {\"value\": 0.21273940879644182}, {\"value\": -0.3362058000726256}, {\"value\": 0.32849826828730716}, {\"value\": -0.4200878078631223}, {\"value\": 0.4442364537442683}, {\"value\": -0.7715998164083223}, {\"value\": -0.09807695315448994}, {\"value\": -0.4151722213823092}, {\"value\": 0.7155331431765006}, {\"value\": 1.6457804522805737}, {\"value\": 0.4656194695101086}, {\"value\": -2.0467397170593835}, {\"value\": 0.4073916876997995}, {\"value\": 0.26734510214178236}, {\"value\": 0.05262263429974702}, {\"value\": -0.47147436504161994}, {\"value\": 0.9273477124754832}, {\"value\": 0.18511129305203536}, {\"value\": 0.9115541627217436}, {\"value\": -0.36932897669001036}, {\"value\": 1.0203933365278113}, {\"value\": 0.3924359167496101}, {\"value\": -0.33244689788468323}, {\"value\": -0.29004824972838555}, {\"value\": -0.8606351384596322}, {\"value\": -1.6555106198643497}, {\"value\": -0.5499147494742774}, {\"value\": -0.22015119000667577}, {\"value\": 0.49177835486687377}, {\"value\": -0.9030030361143557}, {\"value\": -0.6654647316977277}, {\"value\": 0.8958201613227029}, {\"value\": -0.3786016569454203}, {\"value\": -0.543838499095738}, {\"value\": -0.31067247193532616}, {\"value\": -1.414245460267128}, {\"value\": -0.8938262722620346}, {\"value\": 0.8230988123469893}, {\"value\": 1.2947682843978876}, {\"value\": 0.8341038357434116}, {\"value\": 1.1570620027614988}, {\"value\": -0.4955909060878392}, {\"value\": 0.6919684840088542}, {\"value\": -1.4906648959370223}, {\"value\": -0.028520284303338424}, {\"value\": -0.6328531863100929}, {\"value\": -0.03988344220072607}, {\"value\": -0.048639953060153646}, {\"value\": 1.310565115692675}, {\"value\": 0.4406031011827588}, {\"value\": 0.35459047871616406}, {\"value\": 0.09393205451285659}, {\"value\": 0.5275805253099535}, {\"value\": 3.0424353902048513}, {\"value\": -0.07527968257429109}, {\"value\": -0.42312344396759993}, {\"value\": -0.21712449086901808}, {\"value\": 0.3802434527534547}, {\"value\": -0.30969294322109114}, {\"value\": -0.7314722108980621}, {\"value\": -1.5266175697585462}, {\"value\": -1.9100482942828696}, {\"value\": 1.635192494840846}, {\"value\": -0.7192036416072954}, {\"value\": 0.09158262876252395}, {\"value\": 2.150205400450013}, {\"value\": -0.4274895933205686}, {\"value\": -0.4451803450726384}, {\"value\": 0.11728970282379955}, {\"value\": -0.0268207843146621}, {\"value\": 0.3397811060608488}, {\"value\": -0.22833559371166268}, {\"value\": 0.10962354374018916}, {\"value\": 1.857993864012194}, {\"value\": 0.49119939027458615}, {\"value\": -0.909242717574284}, {\"value\": -1.2455588209532877}, {\"value\": -0.1149709166303239}, {\"value\": 0.28145143968182645}, {\"value\": -0.3164974297709853}, {\"value\": 0.34695466051900203}, {\"value\": -0.7050521998640484}, {\"value\": 0.5830726827642551}, {\"value\": 0.09163659059466368}, {\"value\": 0.3494541446610909}, {\"value\": -0.8769558787069277}, {\"value\": -0.476886517932896}, {\"value\": -1.3204960222043336}, {\"value\": -0.4282582674638196}, {\"value\": 0.2502368023802323}, {\"value\": 0.7494170868011558}, {\"value\": -0.08609494900210485}, {\"value\": 1.5491791812486508}, {\"value\": -0.14105931814386435}, {\"value\": -0.3432216402066638}, {\"value\": 0.04011416460685941}, {\"value\": -0.6046793219351496}, {\"value\": 1.7580400799471108}, {\"value\": 1.5466503839688426}, {\"value\": -0.4389554470213833}, {\"value\": -1.8759127465186731}, {\"value\": 1.1953755707546097}, {\"value\": -0.2908616536691456}, {\"value\": 0.15817220858781178}, {\"value\": 0.20333544991276642}, {\"value\": -1.321665505012235}, {\"value\": -0.9241552897273149}, {\"value\": 0.1483231949862087}, {\"value\": 0.09826532818554458}, {\"value\": 0.08696905445208568}, {\"value\": 1.096204203634675}, {\"value\": 0.2453407631551191}, {\"value\": 0.6630057466494883}, {\"value\": 1.5052086800356352}, {\"value\": 1.4445944124992316}, {\"value\": -0.8640542923015292}, {\"value\": 0.3447223951252571}, {\"value\": -0.3242502293094075}, {\"value\": -0.719664021244342}, {\"value\": -1.2846321140688328}, {\"value\": -1.0594379907972296}, {\"value\": -0.7862575088948974}, {\"value\": -0.44033300763294564}, {\"value\": 0.14702310019860768}, {\"value\": 0.9897942304429636}, {\"value\": -0.5722398532903455}, {\"value\": 0.3924830603209515}, {\"value\": 1.4360202483849824}, {\"value\": -1.5302641407687945}, {\"value\": 0.7166313897540206}, {\"value\": 1.108693464408004}, {\"value\": 1.8518502782914195}, {\"value\": 0.30475716021009214}, {\"value\": 0.6544049210330494}, {\"value\": -0.6012727021188764}, {\"value\": 0.04924583384330498}, {\"value\": -0.5001971922781105}, {\"value\": -0.0922290175889323}, {\"value\": 0.9198615700758265}, {\"value\": 0.527957088447435}, {\"value\": 0.3593987764840088}, {\"value\": -1.1327942536771374}, {\"value\": 1.288841601563235}, {\"value\": -1.1995489147171834}, {\"value\": -1.4250485870373093}, {\"value\": -1.1873013326647737}, {\"value\": -0.022103693076311944}, {\"value\": 1.6972653705349352}, {\"value\": 1.655515304097124}, {\"value\": -0.9276933816952316}, {\"value\": -1.6606127583569699}, {\"value\": 0.10948184514481688}, {\"value\": 0.2036378030899707}, {\"value\": 1.5759644655573768}, {\"value\": 0.05976947628166804}, {\"value\": -1.6974655225378774}, {\"value\": 0.18268814981775383}, {\"value\": 0.15064294374354423}, {\"value\": -0.6915224940819698}, {\"value\": -1.133977434108313}, {\"value\": 0.3484615142280314}, {\"value\": 1.6845554501591196}, {\"value\": -0.7639871713494922}, {\"value\": -0.6645380018656161}, {\"value\": -0.006393492588816269}, {\"value\": -1.674521067205422}, {\"value\": -0.7150715806461805}, {\"value\": -1.6617468197678251}, {\"value\": 1.7805582225001793}, {\"value\": 0.5656686002592539}, {\"value\": 0.40978251396519205}, {\"value\": 0.7814655286904609}, {\"value\": -1.4164783949188235}, {\"value\": -0.03867825789993011}, {\"value\": -0.03380344600446043}, {\"value\": -0.7861315267134767}, {\"value\": -0.39738968693293475}, {\"value\": 0.09350056092346481}, {\"value\": -0.08864329202188684}, {\"value\": 0.33318455347457415}, {\"value\": -1.6375488637644753}, {\"value\": 0.48461439135495077}, {\"value\": 2.6422880048984947}, {\"value\": 0.8138013007458488}, {\"value\": 0.02602663594022467}, {\"value\": 0.30493606888843705}, {\"value\": -0.3146748107643891}, {\"value\": -0.055313995901039366}, {\"value\": 0.22027964382717222}, {\"value\": -0.0402066981234413}, {\"value\": -0.7685864741628766}, {\"value\": 0.45707697843341333}, {\"value\": -0.27344291221429506}, {\"value\": 2.0750437659898666}, {\"value\": 0.15862416897702733}, {\"value\": 0.6065398921222335}, {\"value\": -0.9062984600460529}, {\"value\": 0.8601929286541274}, {\"value\": -1.3836724128543594}, {\"value\": -0.1447069223231183}, {\"value\": -0.5120447456038231}, {\"value\": -2.9746838421682424}, {\"value\": 0.534467646569631}, {\"value\": 1.0750409084050707}, {\"value\": 0.7716990200789858}, {\"value\": -0.5124571070272728}, {\"value\": 1.3861748514200218}, {\"value\": 1.386812683466653}, {\"value\": 1.2621936992001264}, {\"value\": 0.4528967914939092}, {\"value\": -0.6019999762510646}, {\"value\": 1.1592852308877637}, {\"value\": -1.8279655563085269}, {\"value\": 0.3006841271956916}, {\"value\": -1.3846365693087141}, {\"value\": 1.4736227564784672}, {\"value\": -0.8467168980137606}, {\"value\": 0.3204686244449828}, {\"value\": 1.3810892382024125}, {\"value\": -0.8619794640207334}, {\"value\": -0.24155574663679635}, {\"value\": 1.5848406301863738}, {\"value\": 0.5300209167952776}, {\"value\": 0.28006064838429}, {\"value\": -1.158785493866286}, {\"value\": -0.2543289098207366}, {\"value\": -1.7283275472331046}, {\"value\": 2.0601923533435933}, {\"value\": -0.7520533100486658}, {\"value\": 0.10504898901226142}, {\"value\": 0.6972377286613496}, {\"value\": 0.6275259674712709}, {\"value\": 1.8553822588492177}, {\"value\": 0.4090194958781241}, {\"value\": -0.82913392841839}, {\"value\": -1.4366429294247511}, {\"value\": 0.10158875662826716}, {\"value\": 0.24066581292300587}, {\"value\": 0.603296766097909}, {\"value\": -0.9892791207277457}, {\"value\": 0.14551219554172717}, {\"value\": 0.5768629120563291}, {\"value\": 0.3988186460863156}, {\"value\": -0.21413589354649776}, {\"value\": -0.97498257771925}, {\"value\": 0.23821759693988037}, {\"value\": -0.1223184249509517}, {\"value\": -0.1962289319833356}, {\"value\": -2.2756042086757553}, {\"value\": 0.0006182642989590567}, {\"value\": 0.10020955092900188}, {\"value\": 0.8368746833278576}, {\"value\": 0.27953397618764986}, {\"value\": 0.9045985557991358}, {\"value\": 0.15234463267916723}, {\"value\": 0.5359684937628004}, {\"value\": -0.7680963787006774}, {\"value\": -0.022648499063387242}, {\"value\": 1.4176597947187886}, {\"value\": -0.3614453754938342}, {\"value\": 1.1685802480411498}, {\"value\": 0.8922116674122849}, {\"value\": -0.21006512062490662}, {\"value\": 1.5916401968096645}, {\"value\": 1.1368558754263074}, {\"value\": -1.004533831439634}, {\"value\": 0.36883219002879797}, {\"value\": -1.5471151598500743}, {\"value\": -0.3802398398191664}, {\"value\": -0.2681205292022407}, {\"value\": -0.35731872697061995}, {\"value\": 2.569062710751882}, {\"value\": -0.1444882007254322}, {\"value\": -1.524591513775198}, {\"value\": -0.5920268556192098}, {\"value\": -2.232165824894515}, {\"value\": -1.3026115302572927}, {\"value\": 1.7258505524340466}, {\"value\": -0.9027200807076962}, {\"value\": 1.6359690871851358}, {\"value\": 0.45371135794510165}, {\"value\": -0.6897350381635371}, {\"value\": 1.0806499712369084}, {\"value\": 0.4249525871590866}, {\"value\": 0.6021034071808464}, {\"value\": 1.439075562185434}, {\"value\": -0.19481184340385865}, {\"value\": -1.041588532661759}, {\"value\": 0.1857282427731074}, {\"value\": -0.14142347965627203}, {\"value\": -1.3512291858417398}, {\"value\": 0.915846342845277}, {\"value\": 1.9609046110417268}, {\"value\": 0.30142651213420735}, {\"value\": 0.9892748575403337}, {\"value\": 0.8244872850760194}, {\"value\": -1.29217642869077}, {\"value\": -0.1358262755371939}, {\"value\": -0.5281967936428744}, {\"value\": 2.0674285334056277}, {\"value\": -1.1032778898152076}, {\"value\": -0.5629259783433768}, {\"value\": 0.2910753624709487}, {\"value\": -0.7147894047486824}, {\"value\": 2.15527308403922}, {\"value\": 1.2255847012555512}, {\"value\": -0.6591519918802762}, {\"value\": 0.6877670990218921}, {\"value\": 1.308041735756194}, {\"value\": -1.0858675582531045}, {\"value\": 0.036734065798300214}, {\"value\": -0.4016135645971236}, {\"value\": 0.7323928886037341}, {\"value\": 0.8027867807027395}, {\"value\": -0.35891240452958434}, {\"value\": 0.5063475384910799}, {\"value\": 0.11569838938649898}, {\"value\": -0.009071936689012983}, {\"value\": -1.5497875158893026}, {\"value\": 0.29441406594336306}, {\"value\": -0.15353517102605022}, {\"value\": -1.556171108863437}, {\"value\": 0.8285424779882925}, {\"value\": -0.40046814167122086}, {\"value\": -0.7280042700658694}, {\"value\": -0.5372695177641613}, {\"value\": -0.08145240244054643}, {\"value\": -0.562216151414564}, {\"value\": 0.14155714677108822}, {\"value\": 0.6480364920661533}, {\"value\": -0.9010843579210279}, {\"value\": -0.21232614901234093}, {\"value\": -0.7727692307532874}, {\"value\": 1.5923015217197898}, {\"value\": -0.8479959263138276}, {\"value\": 0.9902631165713218}, {\"value\": 0.7675725132151509}, {\"value\": 0.14907696436047177}, {\"value\": 1.1892874908128255}, {\"value\": 0.7709688948936809}, {\"value\": -0.3272049771750696}, {\"value\": -0.23262719930576375}, {\"value\": -0.7981237014147939}, {\"value\": -1.3814039410087167}, {\"value\": 0.6894877993931864}, {\"value\": 0.7927780447101338}, {\"value\": -1.4309436428508182}, {\"value\": 1.2026015118071511}, {\"value\": 2.139480228086953}, {\"value\": -1.1026735009427497}, {\"value\": -0.5957381171614183}, {\"value\": -1.077116930450094}, {\"value\": 0.42799281814670675}, {\"value\": 0.890072907896802}, {\"value\": -0.6515823440249369}, {\"value\": 1.064388001358752}, {\"value\": -1.0385830907071667}, {\"value\": 1.4380987627528272}, {\"value\": 1.0302494872006998}, {\"value\": 0.6564391504134156}, {\"value\": -0.21771967151130026}, {\"value\": -0.06607622029266746}, {\"value\": -2.016062025680919}, {\"value\": -0.23356639692680267}, {\"value\": -1.3801787243346266}, {\"value\": 0.34426364841282747}, {\"value\": -0.5321161931135816}, {\"value\": -0.7847756945770306}, {\"value\": 1.8815666934529185}, {\"value\": 0.6755767983241472}, {\"value\": -0.5694050580795584}, {\"value\": -0.08138700948726915}, {\"value\": -0.26067418271002135}, {\"value\": 1.6207748888487832}, {\"value\": -2.2512358853758245}, {\"value\": -1.3296495619625426}, {\"value\": -1.2152011767068054}, {\"value\": 2.4562279135367606}, {\"value\": 2.084181213918901}, {\"value\": 1.180250954112348}, {\"value\": -0.1449176746154169}, {\"value\": -1.3589685673407914}, {\"value\": -0.5426375841626504}, {\"value\": -2.0930862468526716}, {\"value\": -0.8850150066644197}, {\"value\": 1.7643544812271095}, {\"value\": 1.7421911542339554}, {\"value\": -0.8564625487179907}, {\"value\": -0.926577600174247}, {\"value\": -0.09166774708058918}, {\"value\": 0.23911418019744532}, {\"value\": 0.0710494512166188}, {\"value\": 0.6743940321926034}, {\"value\": -2.098861213143376}, {\"value\": 1.5622241205918972}, {\"value\": 0.6527191927954779}, {\"value\": 0.6047168142749414}, {\"value\": -0.5907325467113668}, {\"value\": 0.5054966952086248}, {\"value\": 0.034791143813494525}, {\"value\": -0.5366398107798941}, {\"value\": -1.7983600567536417}, {\"value\": 0.4704763028712897}, {\"value\": 0.5575089324714184}, {\"value\": 0.12143251345836838}, {\"value\": -0.2674893705150198}, {\"value\": -0.35957498700607804}, {\"value\": 1.8292544043696357}, {\"value\": -0.9349138253848213}, {\"value\": -0.3540524178942388}, {\"value\": -0.8122362986003402}, {\"value\": 0.40965237274212174}, {\"value\": -0.09749610775641729}, {\"value\": 1.7682325953206623}, {\"value\": -0.5220269786481786}, {\"value\": 1.273513760240653}, {\"value\": 1.8105702320085861}, {\"value\": -1.050066697378414}, {\"value\": -0.9534559579619778}, {\"value\": 1.050714580257028}, {\"value\": 1.7700249016635898}, {\"value\": -2.2515641935348913}, {\"value\": 0.012358291829797348}, {\"value\": -0.301633798023595}, {\"value\": 0.6869633461997395}, {\"value\": -0.5565750927217511}, {\"value\": 0.3785386132162797}, {\"value\": 1.4345168637476426}, {\"value\": 0.6210297250829746}, {\"value\": -0.8214538829743282}, {\"value\": 2.3303568241749315}, {\"value\": -0.16539003836109628}, {\"value\": -1.804731778224589}, {\"value\": -0.9442469270155491}, {\"value\": -0.579211429121058}, {\"value\": -0.06434454861761574}, {\"value\": 0.25210798720516087}, {\"value\": -1.5460437992725744}, {\"value\": 1.6281728460147458}, {\"value\": 0.11511216195070231}, {\"value\": 0.7325822481385946}, {\"value\": -0.5918670543530594}, {\"value\": -1.164148734392888}, {\"value\": 0.48459094399366076}, {\"value\": -0.6756822071114122}, {\"value\": -0.7262330244311049}, {\"value\": -0.7664839641767744}, {\"value\": -0.21722390000392602}, {\"value\": -1.0497762042868015}, {\"value\": 1.6631985625047454}, {\"value\": -0.1793548828774612}, {\"value\": 1.4690377734618327}, {\"value\": 0.17481416504879616}, {\"value\": 1.1252052754353923}, {\"value\": -1.5500727997409336}, {\"value\": -0.8922444788197383}, {\"value\": -0.5948936202230036}, {\"value\": 0.8252207066972511}, {\"value\": -0.38145743132027354}, {\"value\": 0.17167488208953277}, {\"value\": 0.32782328782464787}, {\"value\": 0.06862759345518477}, {\"value\": -1.494758323551485}, {\"value\": -0.2589188393068708}, {\"value\": 1.070932627145091}, {\"value\": -0.24173826751627484}, {\"value\": -0.1543547774122831}, {\"value\": -1.4674701754551247}, {\"value\": -0.8299007988346944}, {\"value\": -0.18632716420094958}, {\"value\": 0.5980720592228452}, {\"value\": -0.9243988138367336}, {\"value\": 1.5628840092798595}, {\"value\": -0.26294599100891536}, {\"value\": 3.2285433092401967}, {\"value\": 0.09012557555773669}, {\"value\": -0.5413597975827079}, {\"value\": 0.5976650089001706}, {\"value\": -0.2000064973379175}, {\"value\": -0.5348401581035992}, {\"value\": 0.9851692573612097}, {\"value\": -0.35649737563988376}, {\"value\": 0.5838839380385726}, {\"value\": 0.6826956161868947}, {\"value\": 0.7122756951811754}, {\"value\": 1.6978923870925846}, {\"value\": 0.7485829456935328}, {\"value\": 1.677548958196843}, {\"value\": -0.4103735869962867}, {\"value\": 0.9492512121249307}, {\"value\": 0.8892593233584349}, {\"value\": 0.2001623719948763}, {\"value\": -1.8332631325117716}, {\"value\": 0.40171999713401946}, {\"value\": -0.2837925810869459}, {\"value\": 0.9794397412314945}, {\"value\": -0.002404420701696222}, {\"value\": -0.48046657602822207}, {\"value\": 0.24248291898567145}, {\"value\": -0.8410279054318103}, {\"value\": 0.4305464963920262}, {\"value\": 0.548132695801376}, {\"value\": -0.0046790165613101314}, {\"value\": 0.41891378074753527}, {\"value\": 1.5580688916928458}, {\"value\": -0.5452322117773015}, {\"value\": 1.510993061999346}, {\"value\": 0.4451227632015204}, {\"value\": 0.49443840719954135}, {\"value\": 1.1432715951777646}, {\"value\": -1.588663808104092}, {\"value\": 0.48784435593835196}, {\"value\": 0.20882195254609762}, {\"value\": 0.8856171026161688}, {\"value\": 0.4124002752007411}, {\"value\": 1.1911416341430006}, {\"value\": -0.5200781210346095}, {\"value\": 0.4851041304140076}, {\"value\": 1.7321185361029543}, {\"value\": 1.1380217774279604}, {\"value\": -0.30054390362901134}, {\"value\": -1.0146627406048954}, {\"value\": 0.2356186160492922}, {\"value\": -0.8236259365389865}, {\"value\": -1.0996318653927497}, {\"value\": 0.37394276235250545}, {\"value\": 0.023926578709582393}, {\"value\": -0.11699300345648993}, {\"value\": -0.13663650555540882}, {\"value\": 0.39598376351900916}, {\"value\": 0.09988479796092439}, {\"value\": 1.0978944277850804}, {\"value\": 0.08359145086147907}, {\"value\": -0.5389132443063481}, {\"value\": 1.1541399627347726}, {\"value\": -0.7877002624026678}, {\"value\": 0.9616885677603869}, {\"value\": 0.9641262367425758}, {\"value\": -1.047795739685948}, {\"value\": 1.310302473338227}, {\"value\": 1.3172866521567257}, {\"value\": 0.5033974127108763}, {\"value\": -0.6921982455156275}, {\"value\": 0.017860392807728314}, {\"value\": -1.2450799445275136}, {\"value\": -0.4771461319765043}, {\"value\": -0.21808120412410695}, {\"value\": 0.06801183377987524}, {\"value\": 0.8655846498015062}, {\"value\": 0.6342844621018314}, {\"value\": -0.8556775852614379}, {\"value\": 2.142128818872482}, {\"value\": 0.2175517098646665}, {\"value\": 1.2172641238299657}, {\"value\": 0.8115922058720642}, {\"value\": 1.2691961476489604}, {\"value\": -0.3120609470484849}, {\"value\": 0.4868325208980193}, {\"value\": 1.3036444874079662}, {\"value\": 0.2734159392487261}, {\"value\": 0.5193189854344976}, {\"value\": -0.4943248523800258}, {\"value\": -2.1895976052369934}, {\"value\": 0.2090443304510934}, {\"value\": -0.3949146045407477}, {\"value\": -0.11855030002467618}, {\"value\": -0.7849873792967618}, {\"value\": 2.2104675143923496}, {\"value\": 0.6022275680864569}, {\"value\": 1.5715728189699518}, {\"value\": -0.8559214115555615}, {\"value\": -1.3383222706010247}, {\"value\": -1.1719711218292488}, {\"value\": -1.1071056163382103}, {\"value\": -0.6053259594924477}, {\"value\": 1.8308230506922774}, {\"value\": -0.3938811970804685}, {\"value\": -0.5260115983452719}, {\"value\": -1.0196318413762675}, {\"value\": -1.1090856147653854}, {\"value\": -0.1250444563446748}, {\"value\": 0.1282540716033622}, {\"value\": -0.9239200493765176}, {\"value\": -0.038045874193723996}, {\"value\": -0.06487192537781483}, {\"value\": -0.5134785237136357}, {\"value\": -0.4330983659669885}, {\"value\": -1.0191464359266666}, {\"value\": -1.6557080753763282}, {\"value\": -0.666651757785801}, {\"value\": -1.8156530845500816}, {\"value\": -0.7978953618086786}, {\"value\": 0.1499662855095224}, {\"value\": -1.655532840007057}, {\"value\": -1.2577940089762742}, {\"value\": -0.20831080730547036}, {\"value\": 0.7420788916492985}, {\"value\": -0.9278387822499968}, {\"value\": 0.23996654370610543}, {\"value\": 0.22271566516436855}, {\"value\": 0.3742484025222483}, {\"value\": -0.5734082887610626}, {\"value\": 0.5706936127251694}, {\"value\": 0.6763968772661074}, {\"value\": 0.8399890921302222}, {\"value\": 1.0629360028259527}, {\"value\": 0.19032788117601737}, {\"value\": -0.7090700076216491}, {\"value\": -0.4516713748493395}, {\"value\": -1.1543708263334356}, {\"value\": 0.20508041299384672}, {\"value\": -0.9708421670089235}, {\"value\": 1.0135196439466936}, {\"value\": -1.1445255047653893}, {\"value\": -0.2679718428874799}, {\"value\": -0.07501144818143289}, {\"value\": -0.14672347937966024}, {\"value\": 1.0208123362645043}, {\"value\": 1.1249440129502786}, {\"value\": 0.5524637821707035}, {\"value\": -0.5616731511783573}, {\"value\": 0.9379152065714049}, {\"value\": 0.44206327128810585}, {\"value\": -0.11802102485363622}, {\"value\": -1.1438864570992497}, {\"value\": -0.9506533854969843}, {\"value\": 0.9208599307369836}, {\"value\": -0.14891021629848222}, {\"value\": -0.820867746644149}, {\"value\": 0.1917083785256824}, {\"value\": -0.5780096823193386}, {\"value\": 0.7621848109285994}, {\"value\": 0.21289166759769435}, {\"value\": 0.6048986932597601}, {\"value\": 2.8015974232109455}, {\"value\": 0.8335661242957465}, {\"value\": -1.3075314629355677}, {\"value\": -1.2924771358412115}, {\"value\": 0.32755975555369427}, {\"value\": -1.5783070083512971}, {\"value\": 0.5961353410953174}, {\"value\": 0.025472020130488236}, {\"value\": 1.0504997217726646}, {\"value\": -1.2325876227244263}, {\"value\": 0.31610042412088013}, {\"value\": -1.9579038852791086}, {\"value\": -0.6000791361809628}, {\"value\": -1.141792147899713}, {\"value\": -0.8177031033782115}, {\"value\": -0.15459532069394002}, {\"value\": 0.188236757748509}, {\"value\": 1.1298326188858365}, {\"value\": -0.2087906078334321}, {\"value\": 1.0305420557933085}, {\"value\": -1.7491080966527266}, {\"value\": -1.764267024691014}, {\"value\": -0.12868759534721452}, {\"value\": -0.07162490592517057}, {\"value\": -1.1906464445653435}, {\"value\": 0.9461909749254702}, {\"value\": -1.529216041343496}, {\"value\": -0.15793117399609172}, {\"value\": -1.9843105260894405}, {\"value\": -0.9104286337107586}, {\"value\": -0.40438488207515855}, {\"value\": -0.3177852256820333}, {\"value\": -0.808503849792407}, {\"value\": -0.13815272841048723}, {\"value\": 1.3105108391494384}, {\"value\": 0.20511172651574572}, {\"value\": -1.351653567786527}, {\"value\": 0.23897714032614056}, {\"value\": 1.3164872792469307}, {\"value\": -0.9970239775404175}, {\"value\": -0.4879209401077619}, {\"value\": -1.9211599123983627}, {\"value\": -1.1396698238210747}, {\"value\": -0.016596984513972853}, {\"value\": 0.7244288092114202}, {\"value\": -0.8791732442867931}, {\"value\": -0.640846994745625}, {\"value\": 0.6926428861504691}, {\"value\": -1.652637639358074}, {\"value\": 1.0414484328889766}, {\"value\": 0.686250904266415}, {\"value\": 0.5057296321841427}, {\"value\": 0.5747233096040768}, {\"value\": -0.40253184850006674}, {\"value\": -0.45872246607281275}, {\"value\": -0.9841842807842272}, {\"value\": 1.2749524239056773}, {\"value\": -0.5448875480657861}, {\"value\": 0.3474447772277611}, {\"value\": -0.7361607009346453}, {\"value\": 0.2425529426865568}, {\"value\": -0.7528272791002067}, {\"value\": 0.30928073896365404}, {\"value\": 1.7065178019879854}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Histograms work better here\n",
    "\n",
    "normal_values = pd.DataFrame({\"value\": n.rvs(5000)})\n",
    "\n",
    "alt.Chart(normal_values).mark_bar().encode(\n",
    "    alt.X(\"value\", bin=alt.Bin(maxbins=100)),\n",
    "    y='count()',\n",
    "    color=alt.value('#287E1E'),  # Aside: Note US spelling. Also try \"hex codes\": https://htmlcolorcodes.com/\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<div class=\"alert alert-success\">\n",
    "Note that Altair won't let us directly compute a histogram with more than 5000 rows. To do that, check out this example, which saves the data to a local temporary json file, and then displays from that. Without doing this, Altair embeds a *copy* of the data in a graph!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-93a1770baf4f4100a039c0c65c5f6bee.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-93a1770baf4f4100a039c0c65c5f6bee.vega-embed details,\n",
       "  #altair-viz-93a1770baf4f4100a039c0c65c5f6bee.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-93a1770baf4f4100a039c0c65c5f6bee\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-93a1770baf4f4100a039c0c65c5f6bee\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-93a1770baf4f4100a039c0c65c5f6bee\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.20.1?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.20.1\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-9a820c3df49d9ca48e8e2329c00bc905.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.20.1.json\"}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if not alt.data_transformers.active == 'json':  # Check json isn't already active\n",
    "    import os\n",
    "    # Make a temp folder to put these json files in - Altair creates a lot of them!\n",
    "    dataset_temp_name = 'altair-temp-data/'\n",
    "    if not os.path.exists(dataset_temp_name):\n",
    "        # if the folder doesn't exist, create it\n",
    "        os.mkdir(dataset_temp_name)\n",
    "    # Tell Altair to temporary save datasets it needs to that folder\n",
    "    alt.data_transformers.enable('json', prefix=dataset_temp_name)\n",
    "\n",
    "normal_values = pd.DataFrame({\"value\": n.rvs(100000)})\n",
    "\n",
    "alt.Chart(normal_values).mark_bar().encode(\n",
    "    alt.X(\"value\", bin=alt.Bin(maxbins=100)),\n",
    "    y='count()',\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the shape, the famous \"bell curve\" of the normal distribution. It's heavily centred around the mean (0) and the spread of data is indicated by the standard deviation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercises\n",
    "\n",
    "1. Plot a histogram of the standard deviation with the following properties:\n",
    "\n",
    "    1. Mean ($\\mu$) of 1, standard deviation ($\\sigma$) of 7\n",
    "    2. $\\mu=10, \\sigma=1$\n",
    "    3. $\\mu=-10, \\sigma=5$\n",
    "2. Create a python function that accepts two inputs (`mean` and `standard_deviation`) and plots the histogram as per question 1.\n",
    "\n",
    "3. Investigate the documentation of Altair and overlay these plots on top of each other, with different colours, giving a result that looks like this:\n",
    "<img src=\"img/snapshot.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "mean1, std_dev1 = 1, 7  \n",
    "mean2, std_dev2 = 10, 1  \n",
    "mean3, std_dev3 = -10, 5  \n",
    "\n",
    "data1 = np.random.normal(mean1, std_dev1, 1000)\n",
    "data2 = np.random.normal(mean2, std_dev2, 1000)\n",
    "data3 = np.random.normal(mean3, std_dev3, 1000)\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "axs[0].hist(data1, bins=30, density=True, alpha=0.6, color='b')\n",
    "axs[0].set_title('Normal Distribution 1\\n(mean=0, std=1)')\n",
    "axs[0].set_xlabel('Value')\n",
    "axs[0].set_ylabel('Density')\n",
    "\n",
    "axs[1].hist(data2, bins=30, density=True, alpha=0.6, color='g')\n",
    "axs[1].set_title('Normal Distribution 2\\n(mean=1, std=2)')\n",
    "axs[1].set_xlabel('Value')\n",
    "axs[1].set_ylabel('Density')\n",
    "\n",
    "axs[2].hist(data3, bins=30, density=True, alpha=0.6, color='r')\n",
    "axs[2].set_title('Normal Distribution 3\\n(mean=-2, std=0.5)')\n",
    "axs[2].set_xlabel('Value')\n",
    "axs[2].set_ylabel('Density')\n",
    "\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-40d0f0cf1bdf46f8ab89b36518488c16.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-40d0f0cf1bdf46f8ab89b36518488c16.vega-embed details,\n",
       "  #altair-viz-40d0f0cf1bdf46f8ab89b36518488c16.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-40d0f0cf1bdf46f8ab89b36518488c16\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-40d0f0cf1bdf46f8ab89b36518488c16\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-40d0f0cf1bdf46f8ab89b36518488c16\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-1cb17f2eb89525fc84a20fbb90b4aaae.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"title\": \"Normal Distribution histogram with mean 1 and standard deviation 7\", \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-01a9e97e1aaf4e49a7930536dddd0f98.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-01a9e97e1aaf4e49a7930536dddd0f98.vega-embed details,\n",
       "  #altair-viz-01a9e97e1aaf4e49a7930536dddd0f98.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-01a9e97e1aaf4e49a7930536dddd0f98\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-01a9e97e1aaf4e49a7930536dddd0f98\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-01a9e97e1aaf4e49a7930536dddd0f98\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-4138241a11c1f79e076acebbe4cbf64c.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"title\": \"Normal Distribution histogram with mean 10 and standard deviation 1\", \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-2c42447db68d48638ed8443a283ade97.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-2c42447db68d48638ed8443a283ade97.vega-embed details,\n",
       "  #altair-viz-2c42447db68d48638ed8443a283ade97.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-2c42447db68d48638ed8443a283ade97\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-2c42447db68d48638ed8443a283ade97\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-2c42447db68d48638ed8443a283ade97\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-14656ade87b5d77bf96f3e0cac0d9578.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"title\": \"Normal Distribution histogram with mean -10 and standard deviation 5\", \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (1)\n",
    "import pandas as pd\n",
    "from numpy.random import default_rng\n",
    "import altair as alt\n",
    "alt.renderers.enable('default')\n",
    "\n",
    "mean_std_list = [(1,7), (10,1), (-10,5)]\n",
    "rng = default_rng(2024)\n",
    "\n",
    "\n",
    "for vals in mean_std_list:\n",
    "    norm_dist_func = stats.norm(vals[0], vals[1])\n",
    "    results = rng.normal(vals[0], vals[1], 1000)\n",
    "    normal_values = pd.DataFrame({\"value\": results})\n",
    "    norm_plot = alt.Chart(normal_values, title=\"Normal Distribution histogram with mean \" + str(vals[0]) + \" and standard deviation \" + str(vals[1])).mark_bar().encode(\n",
    "    alt.X(\"value\", bin=alt.Bin(maxbins=100)),\n",
    "    y='count()',)\n",
    "    norm_plot.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-01897036578b4edb93936d9c51cb008a.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-01897036578b4edb93936d9c51cb008a.vega-embed details,\n",
       "  #altair-viz-01897036578b4edb93936d9c51cb008a.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-01897036578b4edb93936d9c51cb008a\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-01897036578b4edb93936d9c51cb008a\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-01897036578b4edb93936d9c51cb008a\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-a484195b8908187c70a43751fa536ef8.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"value\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"title\": \"Normal Distribution histogram with mean 1 and standard deviation 2\", \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (2)\n",
    "def display_norm(mean, std):\n",
    "    norm_dist_func = stats.norm(mean, std)\n",
    "    results = norm_dist_func.rvs(1000)\n",
    "    normal_values = pd.DataFrame({\"value\": results})\n",
    "    norm_plot = alt.Chart(normal_values, title=\"Normal Distribution histogram with mean \" + str(mean) + \" and standard deviation \" + str(std)).mark_bar().encode(\n",
    "    alt.X(\"value\", bin=alt.Bin(maxbins=100)),\n",
    "    y='count()',)\n",
    "    norm_plot.display()\n",
    "    \n",
    "display_norm(1,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-7e742cb62c564150b5f8738d36227edb.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-7e742cb62c564150b5f8738d36227edb.vega-embed details,\n",
       "  #altair-viz-7e742cb62c564150b5f8738d36227edb.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-7e742cb62c564150b5f8738d36227edb\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-7e742cb62c564150b5f8738d36227edb\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-7e742cb62c564150b5f8738d36227edb\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-ba10808476d179cf9cfe9862afe696fe.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"area\", \"interpolate\": \"step\", \"opacity\": 0.8}, \"encoding\": {\"color\": {\"field\": \"Columns\", \"type\": \"nominal\"}, \"x\": {\"bin\": {\"maxbins\": 300}, \"field\": \"Values\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"stack\": null, \"type\": \"quantitative\"}}, \"transform\": [{\"fold\": [\"Norm 1\", \"Norm 3\"], \"as\": [\"Columns\", \"Values\"]}], \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (3) Compound Histogram Altair\n",
    "df = pd.DataFrame({'Norm 1': stats.norm(1,7).rvs(6000),\n",
    "                   'Norm 2': stats.norm(10,1).rvs(6000),\n",
    "                   'Norm 3': stats.norm(-10,5).rvs(6000)})\n",
    "\n",
    "alt.Chart(df).transform_fold(\n",
    "    ['Norm 1', 'Norm 3'],\n",
    "    as_=['Columns', 'Values']\n",
    ").mark_area(\n",
    "    opacity=0.8,\n",
    "    interpolate='step'\n",
    ").encode(\n",
    "    alt.X('Values:Q', bin=alt.Bin(maxbins=300)),\n",
    "    alt.Y('count()', stack=None),\n",
    "    alt.Color('Columns:N'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/normal_distributions.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability Density Functions\n",
    "\n",
    "The histograms we were looking at above are approximations of what is known as a *Probability Density Function*, or PDF. A PDF shows us the probability of a given value, for a discrete random variable.\n",
    "\n",
    "For a continuous random variable, any *exact* value has a probability of 0 (think about why this is the case). We can only give probabilities for ranges. For a lower bound of $a$ and an upper bound of $b$, we can obtain the probability of a random value lying between $a$ and $b$ by integrating the PDF between those values. For example, if our PDF function is $f(x)$, then the probability of random variable $X$ lying between $a$ and $b$ is given by:\n",
    "\n",
    "$P[a <= X <= b] = \\int_a^b f(x) dx$\n",
    "\n",
    "As an aside, and very informally, you can think of \"the probability of $X=2$\" as being a range *about* 2, say any value between 1.99 and 2.01 (or whatever precision makes sense in the context). Be clear on this definition when you do go to present your findings though, as a formal definition will be needed to replicate your results.\n",
    "\n",
    "We can generate the PDF through the `.pdf` method on a `scipy.stats` distribution. Earlier in this notebook we computed this manually through the equation. Now we let a library do the work for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = stats.norm(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<scipy.stats._distn_infrastructure.rv_continuous_frozen at 0x17d59a66510>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-4, 4, 1000)\n",
    "y = n.pdf(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As with all probabilities, the sum or integral of the probabilities of all possible outcomes must equal one. In a die roll, each outcome (1, 2, 3, 4, 5, 6) has an probability of $\\frac{1}{6}$. Summed, that equals one.\n",
    "\n",
    "In a continuous scenario, the *area under the curve* must sum to 1.0 across the full range. That is:\n",
    "\n",
    "$\\int_{-\\infty}^{\\infty}f(x)dx = 1$\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    Note that the value $f(x)$ is not a probability! It might look like one, but it's the <i>area under the curve</i> that gives us the probability.\n",
    "</div>\n",
    "\n",
    "For a given function, if it is positive or 0 everywhere, and the area under the curve integrates to 1, the function is a valid probability density function.\n",
    "\n",
    "Some functions are valid only under a given domain. For instance, the function $y = ax(b-x)$ is only positive for $0<=x<=b$. In this case, if the area under the curve sums to 1 across that domain, the function is a valid PDF for that domain.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### Exercises\n",
    "Using three different distribution classes in `scipy.stats`, run the following experiment:\n",
    "\n",
    "1. Compute 10,000 random values. Compute and save the mean.\n",
    "2. Repeat step 1, 1,000 times\n",
    "3. Plot the histogram of the mean values and observe the shape.\n",
    "\n",
    "Use the distributions `norm`, `cosine` and `uniform`.\n",
    "\n",
    "This finding is why the normal distribution is so important, and so commonly found in nature.\n",
    "\n",
    "**Hint:** See this example for how to do independent axes with Altair: https://altair-viz.github.io/gallery/layered_plot_with_dual_axis.html?highlight=resolve_scale\n",
    "\n",
    "#### Extended exercise\n",
    "\n",
    "Load a random dataset, and perform the same exercise with the real world data - that is, take the mean of each of 1,000 samples of size 10,000 and plot the histogram. What shaped distribution does it look like?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-bd06a4ce09fa4046a8310399415268d9.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-bd06a4ce09fa4046a8310399415268d9.vega-embed details,\n",
       "  #altair-viz-bd06a4ce09fa4046a8310399415268d9.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-bd06a4ce09fa4046a8310399415268d9\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-bd06a4ce09fa4046a8310399415268d9\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-bd06a4ce09fa4046a8310399415268d9\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-686717efed30c23dd4d3c5b00493cb57.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"normal\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-fbeb9ca7fa1d4c1281895ca922da47ee.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-fbeb9ca7fa1d4c1281895ca922da47ee.vega-embed details,\n",
       "  #altair-viz-fbeb9ca7fa1d4c1281895ca922da47ee.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-fbeb9ca7fa1d4c1281895ca922da47ee\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-fbeb9ca7fa1d4c1281895ca922da47ee\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-fbeb9ca7fa1d4c1281895ca922da47ee\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-d4623a37fe15f94917ad806d9664a33c.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"poisson\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "  #altair-viz-6488fbb47e0345de9ea8144107f2d6ef.vega-embed {\n",
       "    width: 100%;\n",
       "    display: flex;\n",
       "  }\n",
       "\n",
       "  #altair-viz-6488fbb47e0345de9ea8144107f2d6ef.vega-embed details,\n",
       "  #altair-viz-6488fbb47e0345de9ea8144107f2d6ef.vega-embed details summary {\n",
       "    position: relative;\n",
       "  }\n",
       "</style>\n",
       "<div id=\"altair-viz-6488fbb47e0345de9ea8144107f2d6ef\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  var VEGA_DEBUG = (typeof VEGA_DEBUG == \"undefined\") ? {} : VEGA_DEBUG;\n",
       "  (function(spec, embedOpt){\n",
       "    let outputDiv = document.currentScript.previousElementSibling;\n",
       "    if (outputDiv.id !== \"altair-viz-6488fbb47e0345de9ea8144107f2d6ef\") {\n",
       "      outputDiv = document.getElementById(\"altair-viz-6488fbb47e0345de9ea8144107f2d6ef\");\n",
       "    }\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm/vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm/vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm/vega-lite@5.16.3?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm/vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function maybeLoadScript(lib, version) {\n",
       "      var key = `${lib.replace(\"-\", \"\")}_version`;\n",
       "      return (VEGA_DEBUG[key] == version) ?\n",
       "        Promise.resolve(paths[lib]) :\n",
       "        new Promise(function(resolve, reject) {\n",
       "          var s = document.createElement('script');\n",
       "          document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "          s.async = true;\n",
       "          s.onload = () => {\n",
       "            VEGA_DEBUG[key] = version;\n",
       "            return resolve(paths[lib]);\n",
       "          };\n",
       "          s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "          s.src = paths[lib];\n",
       "        });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else {\n",
       "      maybeLoadScript(\"vega\", \"5\")\n",
       "        .then(() => maybeLoadScript(\"vega-lite\", \"5.16.3\"))\n",
       "        .then(() => maybeLoadScript(\"vega-embed\", \"6\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 300, \"continuousHeight\": 300}}, \"data\": {\"url\": \"altair-temp-data/-4908a54084a15ea408fed36370102733.json\", \"format\": {\"type\": \"json\"}}, \"mark\": {\"type\": \"bar\"}, \"encoding\": {\"x\": {\"bin\": {\"maxbins\": 100}, \"field\": \"uniform\", \"type\": \"quantitative\"}, \"y\": {\"aggregate\": \"count\", \"type\": \"quantitative\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.16.3.json\"}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (1)\n",
    "\n",
    "def get_rv_sample_mean(distribution, n_sample = 10000):\n",
    "    samp = distribution.rvs(n_sample)\n",
    "    return samp.mean()\n",
    "\n",
    "\n",
    "def list_of_means(distribution, n_means = 1000, n_sample = 10000):\n",
    "    samp_means = []\n",
    "    for i in range(n_means):\n",
    "        samp_means.append(get_rv_sample_mean(distribution, n_sample))\n",
    "    return samp_means\n",
    "\n",
    "\n",
    "distributions = dict([(\"normal\", stats.norm(0,1)),\n",
    "                 (\"poisson\", stats.poisson(1,1)),\n",
    "                 (\"uniform\", stats.uniform(0, 1))\n",
    "                ])\n",
    "\n",
    "\n",
    "means = pd.DataFrame({distribution_name: list_of_means(distribution)\n",
    "                  for distribution_name, distribution in distributions.items()})\n",
    "\n",
    "\n",
    "for dist in distributions:\n",
    "    nplot = alt.Chart(means[[dist]]).mark_bar().encode(alt.X(dist, bin=alt.Bin(maxbins=100)), y='count()',)\n",
    "    nplot.display()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/plotting_distributions.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cumulative Density Function\n",
    "\n",
    "A cumulative density function (CDF) tells us the probability of a value being less than, or equal to, a given value. A CDF is normally more useful for everyday usage.\n",
    "\n",
    "Here is the CDF for the normal distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "distribution = stats.norm()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-5, 5, 1000)\n",
    "y_cdf = distribution.cdf(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_cdf);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "This graph allows us to compute the probability that a random value is chosen from the normal distribution ($\\mu=0, \\sigma=1$) will be less than or equal to the given $x$ value.\n",
    "\n",
    "For example, to determine the probability a given value is less than or equal to 1.2, we find the $y$ value corresponding to the given $x$ value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "At x=1.2, y=0.885\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_0 = 1.2\n",
    "y_0 = distribution.cdf(x_0)\n",
    "\n",
    "plt.plot(x, y_cdf)\n",
    "plt.plot([x[0], x_0], [y_0, y_0], '--')\n",
    "plt.plot([x_0, x_0], [0, y_0], '--')\n",
    "print(\"At x={0}, y={1:.3f}\".format(x_0, y_0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some major properties of a CDF, defined as $F_X(x)$ are:\n",
    " \n",
    "* The range (the values y can take) are between (and including) 0 and 1. This comes from its use as a probability computation - see the next point. Formally, $0 <= F_X(x) <= 1$ for any value $x$\n",
    "* The likelihood a value is less than or equal to infinity must be 1, and the likelihood it is less than or equal to negative infinity must be 0. Formally, $F_X(-\\infty)=0$ and $F_X(\\infty)=1$\n",
    "* The CDF value is *increasing*. That is, it must have a positive or zero slope (but not a negative one). Formally, $F_X(a) <= F_X(b) \\text{ iff } a < b$\n",
    " \n",
    "Further, if your random variable has a domain, then the CDF is 0 for all values less than the minimum domain, and 1 for any value above the maximum of the domain.\n",
    "\n",
    "To find the probability that a random variable lies within a range, subtract the value of the CDF at the minimum from the value at the maximum:\n",
    "\n",
    "$P(a < X <= b) = F_X(b) - F_X(a)$\n",
    "\n",
    "For a continuous distribution (like the normal distribution), the CDF is a smooth graph. Its shape will vary, but will follow the general pattern as seen above.\n",
    "\n",
    "For a discrete distribution, the graph is still increasing, but represents a \"staircase\", where the value of $F_X(x)$ between valid values remains the same. For example, for a die roll, the value of $F_X(3) == F_X(3.1)$. This makes sense, as no values between 3.0 and 3.1 can be obtained on a die, so the value $P(X<=3)$ must be the same as $P(X<=3.1)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercises\n",
    "\n",
    "1. Plot the relationship between the mean of a normal distribution as $x$ (with a fixed standard deviation of 1), and the area under the curve between 0 and 1 as the $y$ axis.\n",
    "2. Remake the plot, but have the standard deviation vary as $x$, and the mean fixed as 0. How can you characterise the relationship?\n",
    "\n",
    "#### Extended exercise\n",
    "\n",
    "Plot the CDF for rolling two dice, where the x value is the sum of the two dice, and the y value is the CDF for the distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The area between 0 and 1 decreases as the standard deviation increases are values will spread out and hence have less between 0 and 1.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Exercise 1\n",
    "x_values_1 = np.linspace(-5, 5, 1000)\n",
    "distributions_1 = [stats.norm(x, 1) for x in x_values_1]\n",
    "y_1 = np.array([distribution.cdf(1) - distribution.cdf(0)\n",
    "               for distribution in distributions_1])\n",
    "plt.plot(x_values_1, y_1, \"r\")\n",
    "\n",
    "# Exercise 2\n",
    "x_values_2 = np.linspace(0.1, 20, 1000)\n",
    "distributions_2 = [stats.norm(0, x) for x in x_values_2]\n",
    "y_2 = np.array([distribution.cdf(1) - distribution.cdf(0)\n",
    "               for distribution in distributions_2])\n",
    "plt.plot(x_values_2, y_2)\n",
    "print(\"The area between 0 and 1 decreases as the standard deviation increases are values will spread out and hence have less between 0 and 1.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/cdf_relationships.py`*"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.7 64-bit",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.7"
  },
  "vscode": {
   "interpreter": {
    "hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
